example_2D.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/gamma-opt/icnn/blob/main/example_2D.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# mount git hub repo\n",
        "!git clone https://github.com/gamma-opt/icnn.git\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3Seim8oP_8PA",
        "outputId": "394bdede-da1c-4370-c9dc-95b651c5b4d4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Cloning into 'icnn'...\n",
            "remote: Enumerating objects: 29, done.\u001b[K\n",
            "remote: Counting objects: 100% (29/29), done.\u001b[K\n",
            "remote: Compressing objects: 100% (29/29), done.\u001b[K\n",
            "remote: Total 29 (delta 12), reused 0 (delta 0), pack-reused 0 (from 0)\u001b[K\n",
            "Receiving objects: 100% (29/29), 117.99 KiB | 5.36 MiB/s, done.\n",
            "Resolving deltas: 100% (12/12), done.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# install julia\n",
        "%%shell\n",
        "set -e\n",
        "wget -nv https://raw.githubusercontent.com/joaquimg/SBPO2024/main/install_colab.sh -O /tmp/install_colab.sh\n",
        "bash /tmp/install_colab.sh  # Takes ~ 2 minutes"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4ZLTzeXWACfS",
        "outputId": "02442cf1-7889-427d-ad18-b89440dbd5b8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2024-11-21 14:52:17 URL:https://raw.githubusercontent.com/joaquimg/SBPO2024/main/install_colab.sh [1058/1058] -> \"/tmp/install_colab.sh\" [1]\n",
            "Installing Julia 1.10.5 on the current Colab Runtime...\n",
            "2024-11-21 14:52:19 URL:https://julialang-s3.julialang.org/bin/linux/x64/1.10/julia-1.10.5-linux-x86_64.tar.gz [173909866/173909866] -> \"/tmp/julia.tar.gz\" [1]\n",
            "Installing Julia package IJulia...\n",
            "Installing Julia package BenchmarkTools...\n",
            "Installing IJulia kernel...\n",
            "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mInstalling julia kernelspec in /root/.local/share/jupyter/kernels/julia-1.10\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": []
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now,\n",
        "- go to the \"Runtime\" tab\n",
        "- select \"Change runtime type\"\n",
        "- select julia in the \"Runtime type\" dropdown\n",
        "- click \"save\"\n",
        "\n",
        "You might need to refresh the page.\n"
      ],
      "metadata": {
        "id": "z0cNoHUtCjH4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import Pkg\n",
        "Pkg.add(\"Gogeta\")\n",
        "Pkg.add(\"JuMP\")\n",
        "Pkg.add(\"Plots\")\n",
        "Pkg.add(\"JSON\")\n",
        "Pkg.add(\"Alpine\")\n",
        "Pkg.add(\"HiGHS\")\n",
        "Pkg.add(\"Juniper\")\n",
        "Pkg.add(\"Ipopt\")"
      ],
      "metadata": {
        "id": "-bPrglPK_TnM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "15f53ae8-f5f5-45c2-c425-547a83568ba6"
      },
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\u001b[32m\u001b[1m    Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General.toml`\n",
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Accessors ─────────────────── v0.1.41\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ContextVariablesX ─────────── v0.1.3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m NNlib ─────────────────────── v0.9.27\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m MutableArithmetics ────────── v1.6.3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m StaticArrays ──────────────── v1.9.11\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m PDMats ────────────────────── v0.11.32\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m NetworkLayout ─────────────── v0.4.9\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Optimisers ────────────────── v0.3.4\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m StatisticalTraits ─────────── v3.4.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m StatsFuns ─────────────────── v1.3.2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ShowCases ─────────────────── v0.1.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m HypergeometricFunctions ───── v0.3.27\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m CEnum ─────────────────────── v0.5.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m InitialValues ─────────────── v0.3.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m DelimitedFiles ────────────── v1.9.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m EarCut_jll ────────────────── v2.2.4+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ZygoteRules ───────────────── v0.2.7\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ScopedValues ──────────────── v1.3.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m PrettyPrint ───────────────── v0.2.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m GPUArrays ─────────────────── v11.2.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m MLUtils ───────────────────── v0.4.5\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Missings ──────────────────── v1.2.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m RealDot ───────────────────── v0.1.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m IrrationalConstants ───────── v0.2.4\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Functors ──────────────────── v0.4.12\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m IRTools ───────────────────── v0.4.14\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m LLVM ──────────────────────── v9.2.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m MathOptInterface ──────────── v1.35.2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m FLoopsBase ────────────────── v0.1.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Bzip2_jll ─────────────────── v1.0.9+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m SpecialFunctions ──────────── v2.5.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m StaticArraysCore ──────────── v1.4.3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m OneHotArrays ──────────────── v0.2.6\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m PtrArrays ─────────────────── v1.3.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ProgressLogging ───────────── v0.1.4\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Zygote ────────────────────── v0.6.75\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m CodecBzip2 ────────────────── v0.8.5\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m MicroCollections ──────────── v0.2.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m NaNMath ───────────────────── v1.1.2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m MLDataDevices ─────────────── v1.5.3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m NameResolution ────────────── v0.1.5\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m DefineSingletons ──────────── v0.1.2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m TranscodingStreams ────────── v0.11.3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m DataStructures ────────────── v0.18.20\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m CommonSubexpressions ──────── v0.3.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m BangBang ──────────────────── v0.4.3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ChainRules ────────────────── v1.72.2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m MLStyle ───────────────────── v0.4.17\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m StatsAPI ──────────────────── v1.7.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Rmath_jll ─────────────────── v0.5.1+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m CodecZlib ─────────────────── v0.7.6\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m StructTypes ───────────────── v1.11.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m StatsBase ─────────────────── v0.34.4\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Gogeta ────────────────────── v0.3.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m FLoops ────────────────────── v0.2.2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m JuMP ──────────────────────── v1.23.6\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m DiffRules ─────────────────── v1.15.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ArgCheck ──────────────────── v2.4.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m DiffResults ───────────────── v1.1.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m JSON3 ─────────────────────── v1.14.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m TableTraits ───────────────── v1.0.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m HashArrayMappedTries ──────── v0.2.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Setfield ──────────────────── v1.1.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m DataValueInterfaces ───────── v1.0.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m LLVMExtra_jll ─────────────── v0.0.35+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m AbstractFFTs ──────────────── v1.5.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ConstructionBase ──────────── v1.5.8\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m CategoricalArrays ─────────── v0.10.8\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m OrderedCollections ────────── v1.8.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Reexport ──────────────────── v1.2.2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m LogExpFunctions ───────────── v0.3.29\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ChainRulesCore ────────────── v1.25.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m AliasTables ───────────────── v1.1.3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m KernelAbstractions ────────── v0.9.33\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m MacroTools ────────────────── v0.5.15\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Flux ──────────────────────── v0.14.25\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m CompositionsBase ──────────── v0.1.2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m OpenSpecFun_jll ───────────── v0.5.6+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m SparseInverseSubset ───────── v0.1.2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m JuliaVariables ────────────── v0.2.4\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Extents ───────────────────── v0.1.5\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m InverseFunctions ──────────── v0.1.17\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Atomix ────────────────────── v1.1.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m GPUArraysCore ─────────────── v0.2.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m DocStringExtensions ───────── v0.9.3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Transducers ───────────────── v0.4.84\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m UnsafeAtomics ─────────────── v0.3.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Adapt ─────────────────────── v4.1.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m SimpleTraits ──────────────── v0.9.4\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m IterTools ─────────────────── v1.10.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ScientificTypesBase ───────── v3.0.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Tables ────────────────────── v1.12.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m DataAPI ───────────────────── v1.16.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m MLJModelInterface ─────────── v1.11.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Baselet ───────────────────── v0.1.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m IteratorInterfaceExtensions ─ v1.0.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m GeoFormatTypes ────────────── v0.4.4\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m GeometryBasics ────────────── v0.5.2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Rmath ─────────────────────── v0.8.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m StructArrays ──────────────── v0.6.21\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ForwardDiff ───────────────── v0.10.38\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m FillArrays ────────────────── v1.13.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m BSON ──────────────────────── v0.3.9\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m RecipesBase ───────────────── v1.3.4\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m SplittablesBase ───────────── v0.1.15\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Requires ──────────────────── v1.3.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m SortingAlgorithms ─────────── v1.2.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m QuadGK ────────────────────── v2.11.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m EvoTrees ──────────────────── v0.16.9\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Distributions ─────────────── v0.25.117\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m GeoInterface ──────────────── v1.4.1\n",
            "\u001b[32m\u001b[1m    Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Project.toml`\n",
            "  \u001b[90m[8b0c908c] \u001b[39m\u001b[92m+ Gogeta v0.3.0\u001b[39m\n",
            "\u001b[32m\u001b[1m    Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Manifest.toml`\n",
            "  \u001b[90m[621f4979] \u001b[39m\u001b[92m+ AbstractFFTs v1.5.0\u001b[39m\n",
            "  \u001b[90m[7d9f7c33] \u001b[39m\u001b[92m+ Accessors v0.1.41\u001b[39m\n",
            "  \u001b[90m[79e6a3ab] \u001b[39m\u001b[92m+ Adapt v4.1.1\u001b[39m\n",
            "  \u001b[90m[66dad0bd] \u001b[39m\u001b[92m+ AliasTables v1.1.3\u001b[39m\n",
            "  \u001b[90m[dce04be8] \u001b[39m\u001b[92m+ ArgCheck v2.4.0\u001b[39m\n",
            "  \u001b[90m[a9b6321e] \u001b[39m\u001b[92m+ Atomix v1.1.0\u001b[39m\n",
            "  \u001b[90m[fbb218c0] \u001b[39m\u001b[92m+ BSON v0.3.9\u001b[39m\n",
            "  \u001b[90m[198e06fe] \u001b[39m\u001b[92m+ BangBang v0.4.3\u001b[39m\n",
            "  \u001b[90m[9718e550] \u001b[39m\u001b[92m+ Baselet v0.1.1\u001b[39m\n",
            "  \u001b[90m[fa961155] \u001b[39m\u001b[92m+ CEnum v0.5.0\u001b[39m\n",
            "  \u001b[90m[324d7699] \u001b[39m\u001b[92m+ CategoricalArrays v0.10.8\u001b[39m\n",
            "  \u001b[90m[082447d4] \u001b[39m\u001b[92m+ ChainRules v1.72.2\u001b[39m\n",
            "  \u001b[90m[d360d2e6] \u001b[39m\u001b[92m+ ChainRulesCore v1.25.1\u001b[39m\n",
            "  \u001b[90m[523fee87] \u001b[39m\u001b[92m+ CodecBzip2 v0.8.5\u001b[39m\n",
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            "  \u001b[90m[bbf7d656] \u001b[39m\u001b[92m+ CommonSubexpressions v0.3.1\u001b[39m\n",
            "  \u001b[90m[a33af91c] \u001b[39m\u001b[92m+ CompositionsBase v0.1.2\u001b[39m\n",
            "  \u001b[90m[187b0558] \u001b[39m\u001b[92m+ ConstructionBase v1.5.8\u001b[39m\n",
            "  \u001b[90m[6add18c4] \u001b[39m\u001b[92m+ ContextVariablesX v0.1.3\u001b[39m\n",
            "  \u001b[90m[9a962f9c] \u001b[39m\u001b[92m+ DataAPI v1.16.0\u001b[39m\n",
            "  \u001b[90m[864edb3b] \u001b[39m\u001b[92m+ DataStructures v0.18.20\u001b[39m\n",
            "  \u001b[90m[e2d170a0] \u001b[39m\u001b[92m+ DataValueInterfaces v1.0.0\u001b[39m\n",
            "  \u001b[90m[244e2a9f] \u001b[39m\u001b[92m+ DefineSingletons v0.1.2\u001b[39m\n",
            "  \u001b[90m[8bb1440f] \u001b[39m\u001b[92m+ DelimitedFiles v1.9.1\u001b[39m\n",
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            "  \u001b[90m[31c24e10] \u001b[39m\u001b[92m+ Distributions v0.25.117\u001b[39m\n",
            "  \u001b[90m[ffbed154] \u001b[39m\u001b[92m+ DocStringExtensions v0.9.3\u001b[39m\n",
            "  \u001b[90m[f6006082] \u001b[39m\u001b[92m+ EvoTrees v0.16.9\u001b[39m\n",
            "  \u001b[90m[411431e0] \u001b[39m\u001b[92m+ Extents v0.1.5\u001b[39m\n",
            "  \u001b[90m[cc61a311] \u001b[39m\u001b[92m+ FLoops v0.2.2\u001b[39m\n",
            "  \u001b[90m[b9860ae5] \u001b[39m\u001b[92m+ FLoopsBase v0.1.1\u001b[39m\n",
            "  \u001b[90m[1a297f60] \u001b[39m\u001b[92m+ FillArrays v1.13.0\u001b[39m\n",
            "\u001b[33m⌅\u001b[39m \u001b[90m[587475ba] \u001b[39m\u001b[92m+ Flux v0.14.25\u001b[39m\n",
            "  \u001b[90m[f6369f11] \u001b[39m\u001b[92m+ ForwardDiff v0.10.38\u001b[39m\n",
            "\u001b[33m⌅\u001b[39m \u001b[90m[d9f16b24] \u001b[39m\u001b[92m+ Functors v0.4.12\u001b[39m\n",
            "  \u001b[90m[0c68f7d7] \u001b[39m\u001b[92m+ GPUArrays v11.2.1\u001b[39m\n",
            "  \u001b[90m[46192b85] \u001b[39m\u001b[92m+ GPUArraysCore v0.2.0\u001b[39m\n",
            "  \u001b[90m[68eda718] \u001b[39m\u001b[92m+ GeoFormatTypes v0.4.4\u001b[39m\n",
            "  \u001b[90m[cf35fbd7] \u001b[39m\u001b[92m+ GeoInterface v1.4.1\u001b[39m\n",
            "  \u001b[90m[5c1252a2] \u001b[39m\u001b[92m+ GeometryBasics v0.5.2\u001b[39m\n",
            "  \u001b[90m[8b0c908c] \u001b[39m\u001b[92m+ Gogeta v0.3.0\u001b[39m\n",
            "  \u001b[90m[076d061b] \u001b[39m\u001b[92m+ HashArrayMappedTries v0.2.0\u001b[39m\n",
            "  \u001b[90m[34004b35] \u001b[39m\u001b[92m+ HypergeometricFunctions v0.3.27\u001b[39m\n",
            "  \u001b[90m[7869d1d1] \u001b[39m\u001b[92m+ IRTools v0.4.14\u001b[39m\n",
            "  \u001b[90m[22cec73e] \u001b[39m\u001b[92m+ InitialValues v0.3.1\u001b[39m\n",
            "  \u001b[90m[3587e190] \u001b[39m\u001b[92m+ InverseFunctions v0.1.17\u001b[39m\n",
            "  \u001b[90m[92d709cd] \u001b[39m\u001b[92m+ IrrationalConstants v0.2.4\u001b[39m\n",
            "  \u001b[90m[c8e1da08] \u001b[39m\u001b[92m+ IterTools v1.10.0\u001b[39m\n",
            "  \u001b[90m[82899510] \u001b[39m\u001b[92m+ IteratorInterfaceExtensions v1.0.0\u001b[39m\n",
            "  \u001b[90m[0f8b85d8] \u001b[39m\u001b[92m+ JSON3 v1.14.1\u001b[39m\n",
            "  \u001b[90m[4076af6c] \u001b[39m\u001b[92m+ JuMP v1.23.6\u001b[39m\n",
            "  \u001b[90m[b14d175d] \u001b[39m\u001b[92m+ JuliaVariables v0.2.4\u001b[39m\n",
            "  \u001b[90m[63c18a36] \u001b[39m\u001b[92m+ KernelAbstractions v0.9.33\u001b[39m\n",
            "  \u001b[90m[929cbde3] \u001b[39m\u001b[92m+ LLVM v9.2.0\u001b[39m\n",
            "  \u001b[90m[2ab3a3ac] \u001b[39m\u001b[92m+ LogExpFunctions v0.3.29\u001b[39m\n",
            "\u001b[32m⌃\u001b[39m \u001b[90m[7e8f7934] \u001b[39m\u001b[92m+ MLDataDevices v1.5.3\u001b[39m\n",
            "  \u001b[90m[e80e1ace] \u001b[39m\u001b[92m+ MLJModelInterface v1.11.0\u001b[39m\n",
            "  \u001b[90m[d8e11817] \u001b[39m\u001b[92m+ MLStyle v0.4.17\u001b[39m\n",
            "  \u001b[90m[f1d291b0] \u001b[39m\u001b[92m+ MLUtils v0.4.5\u001b[39m\n",
            "  \u001b[90m[1914dd2f] \u001b[39m\u001b[92m+ MacroTools v0.5.15\u001b[39m\n",
            "  \u001b[90m[b8f27783] \u001b[39m\u001b[92m+ MathOptInterface v1.35.2\u001b[39m\n",
            "  \u001b[90m[128add7d] \u001b[39m\u001b[92m+ MicroCollections v0.2.0\u001b[39m\n",
            "  \u001b[90m[e1d29d7a] \u001b[39m\u001b[92m+ Missings v1.2.0\u001b[39m\n",
            "  \u001b[90m[d8a4904e] \u001b[39m\u001b[92m+ MutableArithmetics v1.6.3\u001b[39m\n",
            "  \u001b[90m[872c559c] \u001b[39m\u001b[92m+ NNlib v0.9.27\u001b[39m\n",
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            "  \u001b[90m[71a1bf82] \u001b[39m\u001b[92m+ NameResolution v0.1.5\u001b[39m\n",
            "  \u001b[90m[46757867] \u001b[39m\u001b[92m+ NetworkLayout v0.4.9\u001b[39m\n",
            "  \u001b[90m[0b1bfda6] \u001b[39m\u001b[92m+ OneHotArrays v0.2.6\u001b[39m\n",
            "\u001b[33m⌅\u001b[39m \u001b[90m[3bd65402] \u001b[39m\u001b[92m+ Optimisers v0.3.4\u001b[39m\n",
            "  \u001b[90m[bac558e1] \u001b[39m\u001b[92m+ OrderedCollections v1.8.0\u001b[39m\n",
            "  \u001b[90m[90014a1f] \u001b[39m\u001b[92m+ PDMats v0.11.32\u001b[39m\n",
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            "  \u001b[90m[33c8b6b6] \u001b[39m\u001b[92m+ ProgressLogging v0.1.4\u001b[39m\n",
            "  \u001b[90m[43287f4e] \u001b[39m\u001b[92m+ PtrArrays v1.3.0\u001b[39m\n",
            "  \u001b[90m[1fd47b50] \u001b[39m\u001b[92m+ QuadGK v2.11.1\u001b[39m\n",
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            "  \u001b[90m[3cdcf5f2] \u001b[39m\u001b[92m+ RecipesBase v1.3.4\u001b[39m\n",
            "  \u001b[90m[189a3867] \u001b[39m\u001b[92m+ Reexport v1.2.2\u001b[39m\n",
            "  \u001b[90m[ae029012] \u001b[39m\u001b[92m+ Requires v1.3.0\u001b[39m\n",
            "  \u001b[90m[79098fc4] \u001b[39m\u001b[92m+ Rmath v0.8.0\u001b[39m\n",
            "  \u001b[90m[30f210dd] \u001b[39m\u001b[92m+ ScientificTypesBase v3.0.0\u001b[39m\n",
            "  \u001b[90m[7e506255] \u001b[39m\u001b[92m+ ScopedValues v1.3.0\u001b[39m\n",
            "  \u001b[90m[efcf1570] \u001b[39m\u001b[92m+ Setfield v1.1.1\u001b[39m\n",
            "  \u001b[90m[605ecd9f] \u001b[39m\u001b[92m+ ShowCases v0.1.0\u001b[39m\n",
            "  \u001b[90m[699a6c99] \u001b[39m\u001b[92m+ SimpleTraits v0.9.4\u001b[39m\n",
            "  \u001b[90m[a2af1166] \u001b[39m\u001b[92m+ SortingAlgorithms v1.2.1\u001b[39m\n",
            "  \u001b[90m[dc90abb0] \u001b[39m\u001b[92m+ SparseInverseSubset v0.1.2\u001b[39m\n",
            "  \u001b[90m[276daf66] \u001b[39m\u001b[92m+ SpecialFunctions v2.5.0\u001b[39m\n",
            "  \u001b[90m[171d559e] \u001b[39m\u001b[92m+ SplittablesBase v0.1.15\u001b[39m\n",
            "  \u001b[90m[90137ffa] \u001b[39m\u001b[92m+ StaticArrays v1.9.11\u001b[39m\n",
            "  \u001b[90m[1e83bf80] \u001b[39m\u001b[92m+ StaticArraysCore v1.4.3\u001b[39m\n",
            "  \u001b[90m[64bff920] \u001b[39m\u001b[92m+ StatisticalTraits v3.4.0\u001b[39m\n",
            "  \u001b[90m[82ae8749] \u001b[39m\u001b[92m+ StatsAPI v1.7.0\u001b[39m\n",
            "  \u001b[90m[2913bbd2] \u001b[39m\u001b[92m+ StatsBase v0.34.4\u001b[39m\n",
            "  \u001b[90m[4c63d2b9] \u001b[39m\u001b[92m+ StatsFuns v1.3.2\u001b[39m\n",
            "\u001b[32m⌃\u001b[39m \u001b[90m[09ab397b] \u001b[39m\u001b[92m+ StructArrays v0.6.21\u001b[39m\n",
            "  \u001b[90m[856f2bd8] \u001b[39m\u001b[92m+ StructTypes v1.11.0\u001b[39m\n",
            "  \u001b[90m[3783bdb8] \u001b[39m\u001b[92m+ TableTraits v1.0.1\u001b[39m\n",
            "  \u001b[90m[bd369af6] \u001b[39m\u001b[92m+ Tables v1.12.0\u001b[39m\n",
            "  \u001b[90m[3bb67fe8] \u001b[39m\u001b[92m+ TranscodingStreams v0.11.3\u001b[39m\n",
            "  \u001b[90m[28d57a85] \u001b[39m\u001b[92m+ Transducers v0.4.84\u001b[39m\n",
            "  \u001b[90m[013be700] \u001b[39m\u001b[92m+ UnsafeAtomics v0.3.0\u001b[39m\n",
            "\u001b[33m⌅\u001b[39m \u001b[90m[e88e6eb3] \u001b[39m\u001b[92m+ Zygote v0.6.75\u001b[39m\n",
            "  \u001b[90m[700de1a5] \u001b[39m\u001b[92m+ ZygoteRules v0.2.7\u001b[39m\n",
            "  \u001b[90m[6e34b625] \u001b[39m\u001b[92m+ Bzip2_jll v1.0.9+0\u001b[39m\n",
            "  \u001b[90m[5ae413db] \u001b[39m\u001b[92m+ EarCut_jll v2.2.4+0\u001b[39m\n",
            "  \u001b[90m[dad2f222] \u001b[39m\u001b[92m+ LLVMExtra_jll v0.0.35+0\u001b[39m\n",
            "  \u001b[90m[efe28fd5] \u001b[39m\u001b[92m+ OpenSpecFun_jll v0.5.6+0\u001b[39m\n",
            "  \u001b[90m[f50d1b31] \u001b[39m\u001b[92m+ Rmath_jll v0.5.1+0\u001b[39m\n",
            "  \u001b[90m[8ba89e20] \u001b[39m\u001b[92m+ Distributed\u001b[39m\n",
            "  \u001b[90m[9fa8497b] \u001b[39m\u001b[92m+ Future\u001b[39m\n",
            "  \u001b[90m[4af54fe1] \u001b[39m\u001b[92m+ LazyArtifacts\u001b[39m\n",
            "  \u001b[90m[4607b0f0] \u001b[39m\u001b[92m+ SuiteSparse\u001b[39m\n",
            "  \u001b[90m[05823500] \u001b[39m\u001b[92m+ OpenLibm_jll v0.8.1+2\u001b[39m\n",
            "\u001b[36m\u001b[1m        Info\u001b[22m\u001b[39m Packages marked with \u001b[32m⌃\u001b[39m and \u001b[33m⌅\u001b[39m have new versions available. Those with \u001b[32m⌃\u001b[39m may be upgradable, but those with \u001b[33m⌅\u001b[39m are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`\n",
            "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mScientificTypesBase\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mAbstractFFTs\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mIteratorInterfaceExtensions\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mStructTypes\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mGeoFormatTypes\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mStatsAPI\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mCEnum\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mInitialValues\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mInverseFunctions\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mFillArrays\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mPrettyPrint\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mUnsafeAtomics\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mArgCheck\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mShowCases\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mIterTools\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mOrderedCollections\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mRequires\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mDataValueInterfaces\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mRealDot\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mReexport\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mDocStringExtensions\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mCompositionsBase\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mExtents\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mIrrationalConstants\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mPtrArrays\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mMacroTools\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mHashArrayMappedTries\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mTranscodingStreams\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mChainRulesCore\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mDefineSingletons\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mNaNMath\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mContextVariablesX\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mDelimitedFiles\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mBSON\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mConstructionBase\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mDataAPI\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mProgressLogging\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mFunctors\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mStaticArraysCore\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mSuiteSparse\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mBaselet\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mRecipesBase\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mBzip2_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mRmath_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mEarCut_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mLLVMExtra_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mOpenSpecFun_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mStatisticalTraits\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mAbstractFFTs → AbstractFFTsTestExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mTableTraits\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mMutableArithmetics\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mInverseFunctions → InverseFunctionsDatesExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mFillArrays → FillArraysSparseArraysExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mNameResolution\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mDataStructures\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mAdapt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mLogExpFunctions\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mAliasTables\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mCommonSubexpressions\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mChainRulesCore → ChainRulesCoreSparseArraysExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mAbstractFFTs → AbstractFFTsChainRulesCoreExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mFLoopsBase\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mConstructionBase → ConstructionBaseLinearAlgebraExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mJSON3\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mMissings\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mGeoInterface\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mDiffResults\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mPDMats\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mSparseInverseSubset\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mCodecBzip2\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mRmath\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mMLJModelInterface\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mTables\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mInverseFunctions → InverseFunctionsTestExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mCompositionsBase → CompositionsBaseInverseFunctionsExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mStaticArrays\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mFillArrays → FillArraysStatisticsExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mLLVM\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mLogExpFunctions → LogExpFunctionsInverseFunctionsExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mSortingAlgorithms\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mQuadGK\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mLogExpFunctions → LogExpFunctionsChainRulesCoreExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mOptimisers\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mFillArrays → FillArraysPDMatsExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mCategoricalArrays\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mStaticArrays → StaticArraysChainRulesCoreExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mStaticArrays → StaticArraysStatisticsExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mConstructionBase → ConstructionBaseStaticArraysExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mAdapt → AdaptStaticArraysExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mJuliaVariables\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mUnsafeAtomics → UnsafeAtomicsLLVM\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mCategoricalArrays → CategoricalArraysJSONExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mSpecialFunctions\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mCategoricalArrays → CategoricalArraysStructTypesExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mStatsBase\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mCategoricalArrays → CategoricalArraysRecipesBaseExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mSetfield\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mStructArrays\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mStructArrays → StructArraysLinearAlgebraExt\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mAccessors → LinearAlgebraExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mMLDataDevices → MLDataDevicesChainRulesCoreExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mMLDataDevices → MLDataDevicesFillArraysExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mMLDataDevices → MLDataDevicesSparseArraysExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mStructArrays → StructArraysAdaptExt\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mStructArrays → StructArraysStaticArraysExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mHypergeometricFunctions\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mAccessors → TestExt\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mKernelAbstractions → LinearAlgebraExt\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mStatsFuns → StatsFunsInverseFunctionsExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mForwardDiff\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mKernelAbstractions → SparseArraysExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mStatsFuns → StatsFunsChainRulesCoreExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mGeometryBasics\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mStructArrays → StructArraysGPUArraysCoreExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mBangBang → BangBangStaticArraysExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mBangBang → BangBangChainRulesCoreExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mBangBang → BangBangTablesExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mForwardDiff → ForwardDiffStaticArraysExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mGPUArrays\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mNetworkLayout\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mNNlib\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mDistributions\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mBangBang → BangBangStructArraysExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mMLDataDevices → MLDataDevicesGPUArraysExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mNNlib → NNlibForwardDiffExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mDistributions → DistributionsTestExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mDistributions → DistributionsChainRulesCoreExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mChainRules\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mMicroCollections\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mOneHotArrays\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mMLDataDevices → MLDataDevicesChainRulesExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mEvoTrees\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mTransducers\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mMLDataDevices → MLDataDevicesOneHotArraysExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mTransducers → TransducersAdaptExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mFLoops\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mMLUtils\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mMLDataDevices → MLDataDevicesMLUtilsExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mZygote\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mMLDataDevices → MLDataDevicesZygoteExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mFlux\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mMathOptInterface\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mJuMP\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39mGogeta\n",
            "  163 dependencies successfully precompiled in 336 seconds. 26 already precompiled.\n",
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m    Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Project.toml`\n",
            "  \u001b[90m[4076af6c] \u001b[39m\u001b[92m+ JuMP v1.23.6\u001b[39m\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m JpegTurbo_jll ──────────────── v3.1.1+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m x265_jll ───────────────────── v3.5.0+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m GR_jll ─────────────────────── v0.73.12+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Libmount_jll ───────────────── v2.40.3+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m libdecor_jll ───────────────── v0.2.2+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m LoggingExtras ──────────────── v1.1.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m LERC_jll ───────────────────── v4.0.1+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m libfdk_aac_jll ─────────────── v2.0.3+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Unitful ────────────────────── v1.22.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_xkbcomp_jll ───────────── v1.4.6+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m RelocatableFolders ─────────── v1.0.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ConcurrentUtilities ────────── v2.4.3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Opus_jll ───────────────────── v1.3.3+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Measures ───────────────────── v0.3.2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Contour ────────────────────── v0.6.3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m OpenSSL ────────────────────── v1.4.3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_xcb_util_wm_jll ───────── v0.4.1+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m RecipesPipeline ────────────── v0.6.12\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Grisu ──────────────────────── v1.0.2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_xcb_util_image_jll ────── v0.4.0+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m PlotUtils ──────────────────── v1.4.3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_libpthread_stubs_jll ──── v0.1.2+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m HTTP ───────────────────────── v1.10.15\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ColorSchemes ───────────────── v3.28.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_libSM_jll ─────────────── v1.2.4+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Fontconfig_jll ─────────────── v2.15.0+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_xcb_util_jll ──────────── v0.4.0+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m GR ─────────────────────────── v0.73.12\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_libxkbfile_jll ────────── v1.1.2+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Cairo_jll ──────────────────── v1.18.2+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Libgpg_error_jll ───────────── v1.51.1+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m EpollShim_jll ──────────────── v0.0.20230411+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_libXinerama_jll ───────── v1.1.5+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m SimpleBufferStream ─────────── v1.2.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_xcb_util_keysyms_jll ──── v0.4.0+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Pipe ───────────────────────── v1.3.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_libXau_jll ────────────── v1.0.12+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m FFMPEG ─────────────────────── v0.4.2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Showoff ────────────────────── v1.0.3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m HarfBuzz_jll ───────────────── v8.5.0+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Pango_jll ──────────────────── v1.55.5+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m xkbcommon_jll ──────────────── v1.4.1+2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m FriBidi_jll ────────────────── v1.0.16+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m UnicodeFun ─────────────────── v0.4.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m XZ_jll ─────────────────────── v5.6.4+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m PlotThemes ─────────────────── v3.3.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m LZO_jll ────────────────────── v2.10.3+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m fzf_jll ────────────────────── v0.56.3+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m FreeType2_jll ──────────────── v2.13.3+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m JLFzf ──────────────────────── v0.1.9\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m GLFW_jll ───────────────────── v3.4.0+2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ExceptionUnwrapping ────────── v0.1.11\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Colors ─────────────────────── v0.13.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m libaom_jll ─────────────────── v3.11.0+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Scratch ────────────────────── v1.2.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m x264_jll ───────────────────── v2021.5.5+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m mtdev_jll ──────────────────── v1.1.6+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_libXext_jll ───────────── v1.3.6+3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_libxcb_jll ────────────── v1.17.0+3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ColorTypes ─────────────────── v0.12.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m libpng_jll ─────────────────── v1.6.46+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Zstd_jll ───────────────────── v1.5.7+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Expat_jll ──────────────────── v2.6.4+3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m TensorCore ─────────────────── v0.1.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Dbus_jll ───────────────────── v1.14.10+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m gperf_jll ──────────────────── v3.1.1+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m eudev_jll ──────────────────── v3.2.9+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Plots ──────────────────────── v1.40.9\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Libtiff_jll ────────────────── v4.7.1+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Format ─────────────────────── v1.3.7\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ColorVectorSpace ───────────── v0.11.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Libffi_jll ─────────────────── v3.2.2+2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_xcb_util_cursor_jll ───── v0.1.4+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m libevdev_jll ───────────────── v1.11.0+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m libinput_jll ───────────────── v1.18.0+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_libXrender_jll ────────── v0.9.11+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Ogg_jll ────────────────────── v1.3.5+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Libuuid_jll ────────────────── v2.40.3+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Vulkan_Loader_jll ──────────── v1.3.243+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Qt6Declarative_jll ─────────── v6.7.1+2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_libXcursor_jll ────────── v1.2.3+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Wayland_protocols_jll ──────── v1.36.0+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_libXi_jll ─────────────── v1.8.2+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_xcb_util_renderutil_jll ─ v0.3.9+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m XML2_jll ───────────────────── v2.13.5+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m XSLT_jll ───────────────────── v1.1.42+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Qt6ShaderTools_jll ─────────── v6.7.1+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m StableRNGs ─────────────────── v1.0.2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m libass_jll ─────────────────── v0.15.2+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Pixman_jll ─────────────────── v0.43.4+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m OpenSSL_jll ────────────────── v3.0.15+3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m BitFlags ───────────────────── v0.1.9\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_libICE_jll ────────────── v1.1.1+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_xtrans_jll ────────────── v1.5.1+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Graphite2_jll ──────────────── v1.3.14+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m LLVMOpenMP_jll ─────────────── v18.1.7+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_xkeyboard_config_jll ──── v2.39.0+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Libgcrypt_jll ──────────────── v1.11.0+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Latexify ───────────────────── v0.16.5\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Gettext_jll ────────────────── v0.21.0+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Wayland_jll ────────────────── v1.21.0+2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m LAME_jll ───────────────────── v3.100.2+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m FixedPointNumbers ──────────── v0.8.5\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_libXrandr_jll ─────────── v1.5.4+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Libiconv_jll ───────────────── v1.18.0+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m URIs ───────────────────────── v1.5.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m LaTeXStrings ───────────────── v1.4.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m FFMPEG_jll ─────────────────── v4.4.4+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Qt6Wayland_jll ─────────────── v6.7.1+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_libXdmcp_jll ──────────── v1.1.5+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Qt6Base_jll ────────────────── v6.7.1+1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m libvorbis_jll ──────────────── v1.3.7+2\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Glib_jll ───────────────────── v2.82.4+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Libglvnd_jll ───────────────── v1.7.0+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_libX11_jll ────────────── v1.8.6+3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Xorg_libXfixes_jll ─────────── v6.0.0+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Unzip ──────────────────────── v0.2.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m UnitfulLatexify ────────────── v1.6.4\n",
            "\u001b[32m\u001b[1m    Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Project.toml`\n",
            "  \u001b[90m[91a5bcdd] \u001b[39m\u001b[92m+ Plots v1.40.9\u001b[39m\n",
            "\u001b[32m\u001b[1m    Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Manifest.toml`\n",
            "  \u001b[90m[d1d4a3ce] \u001b[39m\u001b[92m+ BitFlags v0.1.9\u001b[39m\n",
            "  \u001b[90m[35d6a980] \u001b[39m\u001b[92m+ ColorSchemes v3.28.0\u001b[39m\n",
            "  \u001b[90m[3da002f7] \u001b[39m\u001b[92m+ ColorTypes v0.12.0\u001b[39m\n",
            "  \u001b[90m[c3611d14] \u001b[39m\u001b[92m+ ColorVectorSpace v0.11.0\u001b[39m\n",
            "  \u001b[90m[5ae59095] \u001b[39m\u001b[92m+ Colors v0.13.0\u001b[39m\n",
            "  \u001b[90m[f0e56b4a] \u001b[39m\u001b[92m+ ConcurrentUtilities v2.4.3\u001b[39m\n",
            "  \u001b[90m[d38c429a] \u001b[39m\u001b[92m+ Contour v0.6.3\u001b[39m\n",
            "  \u001b[90m[460bff9d] \u001b[39m\u001b[92m+ ExceptionUnwrapping v0.1.11\u001b[39m\n",
            "  \u001b[90m[c87230d0] \u001b[39m\u001b[92m+ FFMPEG v0.4.2\u001b[39m\n",
            "  \u001b[90m[53c48c17] \u001b[39m\u001b[92m+ FixedPointNumbers v0.8.5\u001b[39m\n",
            "  \u001b[90m[1fa38f19] \u001b[39m\u001b[92m+ Format v1.3.7\u001b[39m\n",
            "  \u001b[90m[28b8d3ca] \u001b[39m\u001b[92m+ GR v0.73.12\u001b[39m\n",
            "  \u001b[90m[42e2da0e] \u001b[39m\u001b[92m+ Grisu v1.0.2\u001b[39m\n",
            "  \u001b[90m[cd3eb016] \u001b[39m\u001b[92m+ HTTP v1.10.15\u001b[39m\n",
            "  \u001b[90m[1019f520] \u001b[39m\u001b[92m+ JLFzf v0.1.9\u001b[39m\n",
            "  \u001b[90m[b964fa9f] \u001b[39m\u001b[92m+ LaTeXStrings v1.4.0\u001b[39m\n",
            "  \u001b[90m[23fbe1c1] \u001b[39m\u001b[92m+ Latexify v0.16.5\u001b[39m\n",
            "  \u001b[90m[e6f89c97] \u001b[39m\u001b[92m+ LoggingExtras v1.1.0\u001b[39m\n",
            "  \u001b[90m[442fdcdd] \u001b[39m\u001b[92m+ Measures v0.3.2\u001b[39m\n",
            "  \u001b[90m[4d8831e6] \u001b[39m\u001b[92m+ OpenSSL v1.4.3\u001b[39m\n",
            "  \u001b[90m[b98c9c47] \u001b[39m\u001b[92m+ Pipe v1.3.0\u001b[39m\n",
            "  \u001b[90m[ccf2f8ad] \u001b[39m\u001b[92m+ PlotThemes v3.3.0\u001b[39m\n",
            "  \u001b[90m[995b91a9] \u001b[39m\u001b[92m+ PlotUtils v1.4.3\u001b[39m\n",
            "  \u001b[90m[91a5bcdd] \u001b[39m\u001b[92m+ Plots v1.40.9\u001b[39m\n",
            "  \u001b[90m[01d81517] \u001b[39m\u001b[92m+ RecipesPipeline v0.6.12\u001b[39m\n",
            "  \u001b[90m[05181044] \u001b[39m\u001b[92m+ RelocatableFolders v1.0.1\u001b[39m\n",
            "  \u001b[90m[6c6a2e73] \u001b[39m\u001b[92m+ Scratch v1.2.1\u001b[39m\n",
            "  \u001b[90m[992d4aef] \u001b[39m\u001b[92m+ Showoff v1.0.3\u001b[39m\n",
            "  \u001b[90m[777ac1f9] \u001b[39m\u001b[92m+ SimpleBufferStream v1.2.0\u001b[39m\n",
            "  \u001b[90m[860ef19b] \u001b[39m\u001b[92m+ StableRNGs v1.0.2\u001b[39m\n",
            "  \u001b[90m[62fd8b95] \u001b[39m\u001b[92m+ TensorCore v0.1.1\u001b[39m\n",
            "  \u001b[90m[5c2747f8] \u001b[39m\u001b[92m+ URIs v1.5.1\u001b[39m\n",
            "  \u001b[90m[1cfade01] \u001b[39m\u001b[92m+ UnicodeFun v0.4.1\u001b[39m\n",
            "  \u001b[90m[1986cc42] \u001b[39m\u001b[92m+ Unitful v1.22.0\u001b[39m\n",
            "  \u001b[90m[45397f5d] \u001b[39m\u001b[92m+ UnitfulLatexify v1.6.4\u001b[39m\n",
            "  \u001b[90m[41fe7b60] \u001b[39m\u001b[92m+ Unzip v0.2.0\u001b[39m\n",
            "  \u001b[90m[83423d85] \u001b[39m\u001b[92m+ Cairo_jll v1.18.2+1\u001b[39m\n",
            "  \u001b[90m[ee1fde0b] \u001b[39m\u001b[92m+ Dbus_jll v1.14.10+0\u001b[39m\n",
            "  \u001b[90m[2702e6a9] \u001b[39m\u001b[92m+ EpollShim_jll v0.0.20230411+1\u001b[39m\n",
            "  \u001b[90m[2e619515] \u001b[39m\u001b[92m+ Expat_jll v2.6.4+3\u001b[39m\n",
            "\u001b[33m⌅\u001b[39m \u001b[90m[b22a6f82] \u001b[39m\u001b[92m+ FFMPEG_jll v4.4.4+1\u001b[39m\n",
            "  \u001b[90m[a3f928ae] \u001b[39m\u001b[92m+ Fontconfig_jll v2.15.0+0\u001b[39m\n",
            "  \u001b[90m[d7e528f0] \u001b[39m\u001b[92m+ FreeType2_jll v2.13.3+1\u001b[39m\n",
            "  \u001b[90m[559328eb] \u001b[39m\u001b[92m+ FriBidi_jll v1.0.16+0\u001b[39m\n",
            "  \u001b[90m[0656b61e] \u001b[39m\u001b[92m+ GLFW_jll v3.4.0+2\u001b[39m\n",
            "  \u001b[90m[d2c73de3] \u001b[39m\u001b[92m+ GR_jll v0.73.12+0\u001b[39m\n",
            "  \u001b[90m[78b55507] \u001b[39m\u001b[92m+ Gettext_jll v0.21.0+0\u001b[39m\n",
            "  \u001b[90m[7746bdde] \u001b[39m\u001b[92m+ Glib_jll v2.82.4+0\u001b[39m\n",
            "  \u001b[90m[3b182d85] \u001b[39m\u001b[92m+ Graphite2_jll v1.3.14+1\u001b[39m\n",
            "  \u001b[90m[2e76f6c2] \u001b[39m\u001b[92m+ HarfBuzz_jll v8.5.0+0\u001b[39m\n",
            "  \u001b[90m[aacddb02] \u001b[39m\u001b[92m+ JpegTurbo_jll v3.1.1+0\u001b[39m\n",
            "  \u001b[90m[c1c5ebd0] \u001b[39m\u001b[92m+ LAME_jll v3.100.2+0\u001b[39m\n",
            "  \u001b[90m[88015f11] \u001b[39m\u001b[92m+ LERC_jll v4.0.1+0\u001b[39m\n",
            "  \u001b[90m[1d63c593] \u001b[39m\u001b[92m+ LLVMOpenMP_jll v18.1.7+0\u001b[39m\n",
            "  \u001b[90m[dd4b983a] \u001b[39m\u001b[92m+ LZO_jll v2.10.3+0\u001b[39m\n",
            "\u001b[33m⌅\u001b[39m \u001b[90m[e9f186c6] \u001b[39m\u001b[92m+ Libffi_jll v3.2.2+2\u001b[39m\n",
            "  \u001b[90m[d4300ac3] \u001b[39m\u001b[92m+ Libgcrypt_jll v1.11.0+0\u001b[39m\n",
            "  \u001b[90m[7e76a0d4] \u001b[39m\u001b[92m+ Libglvnd_jll v1.7.0+0\u001b[39m\n",
            "  \u001b[90m[7add5ba3] \u001b[39m\u001b[92m+ Libgpg_error_jll v1.51.1+0\u001b[39m\n",
            "  \u001b[90m[94ce4f54] \u001b[39m\u001b[92m+ Libiconv_jll v1.18.0+0\u001b[39m\n",
            "  \u001b[90m[4b2f31a3] \u001b[39m\u001b[92m+ Libmount_jll v2.40.3+0\u001b[39m\n",
            "  \u001b[90m[89763e89] \u001b[39m\u001b[92m+ Libtiff_jll v4.7.1+0\u001b[39m\n",
            "  \u001b[90m[38a345b3] \u001b[39m\u001b[92m+ Libuuid_jll v2.40.3+0\u001b[39m\n",
            "  \u001b[90m[e7412a2a] \u001b[39m\u001b[92m+ Ogg_jll v1.3.5+1\u001b[39m\n",
            "  \u001b[90m[458c3c95] \u001b[39m\u001b[92m+ OpenSSL_jll v3.0.15+3\u001b[39m\n",
            "  \u001b[90m[91d4177d] \u001b[39m\u001b[92m+ Opus_jll v1.3.3+0\u001b[39m\n",
            "  \u001b[90m[36c8627f] \u001b[39m\u001b[92m+ Pango_jll v1.55.5+0\u001b[39m\n",
            "\u001b[33m⌅\u001b[39m \u001b[90m[30392449] \u001b[39m\u001b[92m+ Pixman_jll v0.43.4+0\u001b[39m\n",
            "\u001b[33m⌅\u001b[39m \u001b[90m[c0090381] \u001b[39m\u001b[92m+ Qt6Base_jll v6.7.1+1\u001b[39m\n",
            "  \u001b[90m[629bc702] \u001b[39m\u001b[92m+ Qt6Declarative_jll v6.7.1+2\u001b[39m\n",
            "  \u001b[90m[ce943373] \u001b[39m\u001b[92m+ Qt6ShaderTools_jll v6.7.1+1\u001b[39m\n",
            "  \u001b[90m[e99dba38] \u001b[39m\u001b[92m+ Qt6Wayland_jll v6.7.1+1\u001b[39m\n",
            "  \u001b[90m[a44049a8] \u001b[39m\u001b[92m+ Vulkan_Loader_jll v1.3.243+0\u001b[39m\n",
            "  \u001b[90m[a2964d1f] \u001b[39m\u001b[92m+ Wayland_jll v1.21.0+2\u001b[39m\n",
            "  \u001b[90m[2381bf8a] \u001b[39m\u001b[92m+ Wayland_protocols_jll v1.36.0+0\u001b[39m\n",
            "  \u001b[90m[02c8fc9c] \u001b[39m\u001b[92m+ XML2_jll v2.13.5+0\u001b[39m\n",
            "  \u001b[90m[aed1982a] \u001b[39m\u001b[92m+ XSLT_jll v1.1.42+0\u001b[39m\n",
            "  \u001b[90m[ffd25f8a] \u001b[39m\u001b[92m+ XZ_jll v5.6.4+1\u001b[39m\n",
            "  \u001b[90m[f67eecfb] \u001b[39m\u001b[92m+ Xorg_libICE_jll v1.1.1+0\u001b[39m\n",
            "  \u001b[90m[c834827a] \u001b[39m\u001b[92m+ Xorg_libSM_jll v1.2.4+0\u001b[39m\n",
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            "  \u001b[90m[c7cfdc94] \u001b[39m\u001b[92m+ Xorg_libxcb_jll v1.17.0+3\u001b[39m\n",
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            "  \u001b[90m[0d47668e] \u001b[39m\u001b[92m+ Xorg_xcb_util_renderutil_jll v0.3.9+1\u001b[39m\n",
            "  \u001b[90m[c22f9ab0] \u001b[39m\u001b[92m+ Xorg_xcb_util_wm_jll v0.4.1+1\u001b[39m\n",
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            "\u001b[33m⌅\u001b[39m \u001b[90m[1270edf5] \u001b[39m\u001b[92m+ x264_jll v2021.5.5+0\u001b[39m\n",
            "\u001b[33m⌅\u001b[39m \u001b[90m[dfaa095f] \u001b[39m\u001b[92m+ x265_jll v3.5.0+0\u001b[39m\n",
            "  \u001b[90m[d8fb68d0] \u001b[39m\u001b[92m+ xkbcommon_jll v1.4.1+2\u001b[39m\n",
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            "\u001b[36m\u001b[1m        Info\u001b[22m\u001b[39m Packages marked with \u001b[33m⌅\u001b[39m have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`\n",
            "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mTensorCore\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mOpenSSL\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mLatexify → SparseArraysExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mColorTypes\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mColors\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mUnitful\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mColorVectorSpace\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mZygote → ZygoteColorsExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mUnitful → InverseFunctionsUnitfulExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mUnitful → ConstructionBaseUnitfulExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mXorg_xcb_util_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mXorg_libX11_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mColorVectorSpace → SpecialFunctionsExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mAccessors → UnitfulExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mUnitfulLatexify\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mXorg_xcb_util_image_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mXorg_xcb_util_keysyms_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mXorg_xcb_util_renderutil_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mXorg_xcb_util_wm_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mXorg_libXrender_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mXorg_libXext_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mXorg_libXfixes_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mXorg_libxkbfile_jll\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mLibglvnd_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mXorg_libXinerama_jll\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mCairo_jll\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mColorSchemes\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mHarfBuzz_jll\u001b[39m\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mlibdecor_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mVulkan_Loader_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mHTTP\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mFFMPEG\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mGLFW_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mQt6Base_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mQt6ShaderTools_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mGR_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mQt6Declarative_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mQt6Wayland_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mGR\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mPlotUtils\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mPlotThemes\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mRecipesPipeline\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39mPlots\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mPlots → UnitfulExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mPlots → IJuliaExt\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mPlots → GeometryBasicsExt\u001b[39m\n",
            "  127 dependencies successfully precompiled in 215 seconds. 190 already precompiled.\n",
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m    Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Project.toml`\n",
            "  \u001b[90m[682c06a0] \u001b[39m\u001b[92m+ JSON v0.21.4\u001b[39m\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Combinatorics ─ v1.0.2\n",
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            "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mCombinatorics\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39mAlpine\n",
            "  2 dependencies successfully precompiled in 6 seconds. 317 already precompiled.\n",
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            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m HiGHS ───── v1.13.0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m HiGHS_jll ─ v1.9.0+0\n",
            "\u001b[32m\u001b[1m    Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Project.toml`\n",
            "  \u001b[90m[87dc4568] \u001b[39m\u001b[92m+ HiGHS v1.13.0\u001b[39m\n",
            "\u001b[32m\u001b[1m    Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Manifest.toml`\n",
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            "  \u001b[90m[8fd58aa0] \u001b[39m\u001b[92m+ HiGHS_jll v1.9.0+0\u001b[39m\n",
            "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
            "\u001b[32m  ✓ \u001b[39m\u001b[90mHiGHS_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39mHiGHS\n",
            "  2 dependencies successfully precompiled in 20 seconds. 319 already precompiled.\n",
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Juniper ─ v0.9.2\n",
            "\u001b[32m\u001b[1m    Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Project.toml`\n",
            "  \u001b[90m[2ddba703] \u001b[39m\u001b[92m+ Juniper v0.9.2\u001b[39m\n",
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            "  \u001b[90m[2ddba703] \u001b[39m\u001b[92m+ Juniper v0.9.2\u001b[39m\n",
            "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
            "\u001b[32m  ✓ \u001b[39mJuniper\n",
            "  1 dependency successfully precompiled in 3 seconds. 321 already precompiled.\n",
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
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            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Hwloc_jll ────── v2.11.2+3\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Ipopt_jll ────── v300.1400.1700+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m OpenBLAS32_jll ─ v0.3.24+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m MUMPS_seq_jll ── v500.700.301+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m Ipopt ────────── v1.7.1\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m ASL_jll ──────── v0.1.3+0\n",
            "\u001b[32m\u001b[1m   Installed\u001b[22m\u001b[39m SPRAL_jll ────── v2024.5.8+0\n",
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            "  \u001b[90m[b6b21f68] \u001b[39m\u001b[92m+ Ipopt v1.7.1\u001b[39m\n",
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            "  \u001b[90m[d7ed1dd3] \u001b[39m\u001b[92m+ MUMPS_seq_jll v500.700.301+0\u001b[39m\n",
            "\u001b[33m⌅\u001b[39m \u001b[90m[656ef2d0] \u001b[39m\u001b[92m+ OpenBLAS32_jll v0.3.24+0\u001b[39m\n",
            "\u001b[33m⌅\u001b[39m \u001b[90m[319450e9] \u001b[39m\u001b[92m+ SPRAL_jll v2024.5.8+0\u001b[39m\n",
            "\u001b[36m\u001b[1m        Info\u001b[22m\u001b[39m Packages marked with \u001b[33m⌅\u001b[39m have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`\n",
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            "\u001b[32m  ✓ \u001b[39m\u001b[90mIpopt_jll\u001b[39m\n",
            "\u001b[32m  ✓ \u001b[39mIpopt\n",
            "  8 dependencies successfully precompiled in 16 seconds. 322 already precompiled.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "using Gogeta\n",
        "using JuMP\n",
        "using Plots\n",
        "using JSON\n",
        "using Alpine\n",
        "using HiGHS\n",
        "using Juniper\n",
        "using Ipopt\n",
        "\n",
        "# replace with the path to the model_weights.json file\n",
        "filepath = \"icnn/model_weights_2D.json\"\n",
        "\n",
        "# Read the JSON file\n",
        "json_content = read(filepath, String)\n",
        "\n",
        "# Parse the JSON content\n",
        "parsed_json = JSON.parse(json_content)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rHHCjpGPICjR",
        "outputId": "f09196e4-8984-42c4-f7ff-f7a3b4a7f1e7"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Dict{String, Any} with 3 entries:\n",
              "  \"FC2\"   => Any[Any[Any[0.667317], Any[1.52441]], Any[-2.1556]]\n",
              "  \"SKIP2\" => Any[Any[Any[-2.07353]]]\n",
              "  \"FC1\"   => Any[Any[Any[-2.05871, 1.12061]], Any[-0.948954, 2.04866]]"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "A3HKKgGh_NXX",
        "outputId": "f29af8d9-7806-4b65-a9cc-a76100edc1d9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "forwardpass (generic function with 1 method)"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ],
      "source": [
        "#-----------------------------ICNN-------------------------------------------------#\n",
        "\n",
        "# Configure Ipopt to be silent\n",
        "nlp_solver = optimizer_with_attributes(\n",
        "    Ipopt.Optimizer,\n",
        "    \"print_level\" => 0\n",
        ")\n",
        "\n",
        "# Configure Juniper to be silent\n",
        "juniper_solver = optimizer_with_attributes(\n",
        "    Juniper.Optimizer,\n",
        "    \"nl_solver\" => nlp_solver,\n",
        "    \"log_levels\" => []\n",
        ")\n",
        "\n",
        "# Configure HiGHS to be silent\n",
        "milp_solver = optimizer_with_attributes(\n",
        "    HiGHS.Optimizer,\n",
        "    \"output_flag\" => false\n",
        ")\n",
        "\n",
        "# Create the Alpine optimizer with silent logging\n",
        "alpine_optimizer = optimizer_with_attributes(\n",
        "    Alpine.Optimizer,\n",
        "    \"nlp_solver\" => juniper_solver,\n",
        "    \"mip_solver\" => milp_solver,\n",
        "    \"log_level\" => 0  # Ensure Alpine's logging is silent\n",
        ")\n",
        "\n",
        "# define the icnn model\n",
        "icnn_lp =  Model(alpine_optimizer)\n",
        "\n",
        "# define the output variable\n",
        "icnn_output_var = @variable(icnn_lp, z, base_name=\"output_var\")\n",
        "\n",
        "# define the input variable\n",
        "icnn_input_var = @variable(icnn_lp, x, base_name=\"input_var\")\n",
        "\n",
        "# define the objective function\n",
        "@objective(icnn_lp, Min, 0)\n",
        "\n",
        "# define the constraints on input variable\n",
        "@constraint(icnn_lp, x <= 3)\n",
        "@constraint(icnn_lp, x >= -3)\n",
        "\n",
        "# add variables, constraints, and an objective function to the icnn_lp model to account for the generated ICNN.\n",
        "ICNN_incorporate!(icnn_lp, filepath, icnn_output_var, icnn_input_var)\n",
        "\n",
        "function forwardpass(jump_model, input_values)\n",
        "    fix(jump_model[:x], input_values; force = true)\n",
        "    optimize!(jump_model)\n",
        "    return value.(jump_model[:z])\n",
        "end"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "I7cKwi-z_NXY",
        "outputId": "9f338e9a-03f7-4223-e18e-accb76b6044c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "input_var ≥ -3"
            ],
            "text/latex": "$$ input\\_var \\geq -3 $$"
          },
          "metadata": {},
          "execution_count": 4
        }
      ],
      "source": [
        "#---------------------------Out ICNN-----------------------------------------------#\n",
        "# define the outter jump model\n",
        "out_icnn_lp = Model(alpine_optimizer)\n",
        "\n",
        "# define the output variable\n",
        "out_output_var = @variable(out_icnn_lp, z, base_name=\"output_var\")\n",
        "\n",
        "# define the input variable\n",
        "out_input_var = @variable( out_icnn_lp, x, base_name=\"input_var\")\n",
        "\n",
        "# define the objective\n",
        "@objective(out_icnn_lp, Min, 0)\n",
        "\n",
        "# define the constraints on input variable\n",
        "@constraint(out_icnn_lp, x <= 3)\n",
        "@constraint(out_icnn_lp, x >= -3)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "Ujlw3P6v_NXZ",
        "outputId": "2aec4d5f-8b2c-4bdc-94fb-e5d8f5e3f64d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Warning: -/+Inf bounds detected on at least 6 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "******************************************************************************\n",
            "This program contains Ipopt, a library for large-scale nonlinear optimization.\n",
            " Ipopt is released as open source code under the Eclipse Public License (EPL).\n",
            "         For more information visit https://github.com/coin-or/Ipopt\n",
            "******************************************************************************\n",
            "\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "f (generic function with 1 method)"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "#---------------------------Example 1----------------------------------------------#\n",
        "\n",
        "# add contraint on the output variable\n",
        "@constraint(out_icnn_lp, exm_1, z >= 2)\n",
        "\n",
        "# define the objective\n",
        "@objective(out_icnn_lp, Max, x)\n",
        "\n",
        "# add variables, constraints, and an objective function to the out_icnn_lp model to account for the generated ICNN.\n",
        "ICNN_incorporate!(out_icnn_lp, filepath, out_output_var, out_input_var)\n",
        "\n",
        "# optimize the outter jump model\n",
        "optimize!(out_icnn_lp)\n",
        "\n",
        "# save the input and output values\n",
        "x_optimal = value.(out_icnn_lp[:x])\n",
        "out_z_optimal = value.(out_icnn_lp[:z])\n",
        "\n",
        "icnn_z_optimal = forwardpass(icnn_lp, x_optimal)\n",
        "\n",
        "# Define the function f(x) = 2^(-x)\n",
        "f(x) = 2^(-x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "pVETbrKw_NXZ",
        "outputId": "6c741233-75c2-405a-ecae-ca7fd2a29b0b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Max input_var - output_var\n",
            "Subject to\n",
            " -input_var + _[3] = 0\n",
            " output_var - _[6] = 0\n",
            " input_var ≥ -3\n",
            " exm_1 : output_var ≥ 2\n",
            " _[4] ≥ 0\n",
            " _[5] ≥ 0\n",
            " 2.0587143898010254 _[3] + _[4] ≥ -0.9489541053771973\n",
            " -1.120605707168579 _[3] + _[5] ≥ 2.0486631393432617\n",
            " 2.0735292434692383 _[3] - 0.667317271232605 _[4] - 1.5244076251983643 _[5] + _[6] ≥ -2.1556038856506348\n",
            " input_var ≤ 3\n",
            "\n"
          ]
        }
      ],
      "source": [
        "println(out_icnn_lp)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lVmxTCml_NXa",
        "outputId": "649d62b9-44cf-424a-d9af-2fa78847e88d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "# Generate data for plotting\n",
        "x_values = -3:0.1:3\n",
        "y_values = f.(x_values)\n",
        "\n",
        "# Plot the function\n",
        "plot(x_values, y_values, label=\"f(x) = 2^(-x)\", xlabel=\"x\", ylabel=\"z\", title=\"Plot of f(x) = 2^(-x) = z\")\n",
        "\n",
        "# forward pass x_values to the icnn model\n",
        "icnn = forwardpass.(icnn_lp, x_values)\n",
        "# Plot the function\n",
        "plot!(x_values, icnn, label=\"icnn(x)\")\n",
        "\n",
        "plot!(x_values, 2*ones(length(x_values)), label=\"z = 2\")\n",
        "\n",
        "scatter!([x_optimal], [out_z_optimal], label=\"(x*, z*) = max. out_icnn(x)\")\n",
        "scatter!([x_optimal], [icnn_z_optimal], label=\"(x*, icnn(x*))\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1_3lIAbh_NXa",
        "outputId": "d4b78639-2f9d-4c61-82db-8230c47a505b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        }
      },
      "outputs": [
        {
          "output_type": "error",
          "ename": "LoadError",
          "evalue": "",
          "traceback": [
            "",
            "",
            "Stacktrace:",
            " [1] delete(m::MathOptInterface.Utilities.CachingOptimizer{MathOptInterface.Bridges.LazyBridgeOptimizer{Alpine.Optimizer}, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}, index::MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.GreaterThan{Float64}})",
            "   @ MathOptInterface.Utilities ~/.julia/packages/MathOptInterface/gLl4d/src/Utilities/cachingoptimizer.jl:693",
            " [2] delete(model::Model, con_ref::ConstraintRef{Model, MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.GreaterThan{Float64}}, ScalarShape})",
            "   @ JuMP ~/.julia/packages/JuMP/i68GU/src/constraints.jl:568",
            " [3] top-level scope",
            "   @ In[10]:3"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The index MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.GreaterThan{Float64}}(2) is invalid. Note that an index becomes invalid after it has been deleted."
          ]
        }
      ],
      "source": [
        "#---------------------------Example 2---------------------------------------------#\n",
        "\n",
        "delete(out_icnn_lp, exm_1)\n",
        "\n",
        "# define the objective\n",
        "@objective(out_icnn_lp, Max, x+z)\n",
        "\n",
        "# add variables, constraints, and an objective function to the out_icnn_lp model to account for the generated ICNN.\n",
        "ICNN_incorporate!(out_icnn_lp, filepath, out_output_var, out_input_var)\n",
        "\n",
        "# optimize the outter jump model\n",
        "optimize!(out_icnn_lp)\n",
        "\n",
        "# save the input and output values\n",
        "x_optimal = value.(out_icnn_lp[:x])\n",
        "out_z_optimal = value.(out_icnn_lp[:z])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dLGM46_g_NXb",
        "outputId": "7137917b-8c72-4c81-8cea-769b67cad5c9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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          },
          "metadata": {},
          "execution_count": 11
        }
      ],
      "source": [
        "# Define the function f(x) = 2^(-x)\n",
        "f(x) = 2^(-x)\n",
        "\n",
        "# Generate data for plotting\n",
        "x_values = -3:0.1:3\n",
        "y_values = f.(x_values)\n",
        "\n",
        "# Plot the function\n",
        "plot(x_values, y_values, label=\"f(x) = 2^(-x)\", xlabel=\"x\", ylabel=\"z\", title=\"Plot of f(x) = 2^(-x) = z\")\n",
        "\n",
        "#forward pass x_values to the icnn model\n",
        "icnn = forwardpass.(icnn_lp, x_values)\n",
        "# Plot the function\n",
        "plot!(x_values, icnn, label=\"icnn(x)\")\n",
        "\n",
        "# calculate x+z values\n",
        "xz = x_values .+ icnn\n",
        "\n",
        "max_ind = findfirst(x -> x == maximum(xz), xz)\n",
        "scatter!([x_values[max_ind]], [icnn[max_ind]], label=\"x* = max. x + z\")\n",
        "\n",
        "scatter!([x_optimal], [out_z_optimal], label=\"(x*, z*) = max. out_icnn(x)\")"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# define the branching sets\n",
        "extreme_points = [[-3, 0],[0,3]]\n"
      ],
      "metadata": {
        "id": "cd7uET9H_jtk",
        "outputId": "c63fa71f-e11a-40ca-cb31-e73b6a5367af",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2-element Vector{Vector{Int64}}:\n",
              " [-3, 0]\n",
              " [0, 3]"
            ]
          },
          "metadata": {},
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "NsKwYwTKC3Lb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# define a function that generates a copy of icnn_lp and ads new constraints\n",
        "function add_envelope_constraints(filepath, extreme_points, icnn_lp)\n",
        "\n",
        "    # define the icnn model\n",
        "    new_icnn_lp =  Model(alpine_optimizer)\n",
        "\n",
        "    # define the output variable\n",
        "    new_icnn_output_var = @variable(new_icnn_lp, z, base_name=\"output_var\")\n",
        "\n",
        "    # define the input variable\n",
        "    new_icnn_input_var = @variable(new_icnn_lp, x, base_name=\"input_var\")\n",
        "\n",
        "    # define the objective function\n",
        "    @objective(new_icnn_lp, Min, 0)\n",
        "\n",
        "    # define the constraints on input variable\n",
        "    @constraint(new_icnn_lp, x <= extreme_points[2])\n",
        "    @constraint(new_icnn_lp, x >= extreme_points[1])\n",
        "\n",
        "    # add variables, constraints, and an objective function to the icnn_lp model to account for the generated ICNN.\n",
        "    ICNN_incorporate!(new_icnn_lp, filepath, new_icnn_output_var, new_icnn_input_var)\n",
        "\n",
        "    n = length(extreme_points)\n",
        "    @variable(new_icnn_lp, a[1:n] >= 0)  # Constraint 1: ai >= 0\n",
        "\n",
        "    # Constraint 2: x = sum(ai * extreme_points_i)\n",
        "    @constraint(new_icnn_lp, new_icnn_lp[:x] == sum(a[i] * extreme_points[i] for i in 1:n))\n",
        "\n",
        "    # Constraint 3: z_k <= sum(ai * forwardpass(icnn_lp, extreme_points_i))\n",
        "    @constraint(new_icnn_lp, new_icnn_lp[:z] <= sum(a[i] * forwardpass(new_icnn_lp, extreme_points[i]) for i in 1:n))\n",
        "\n",
        "    return new_icnn_lp\n",
        "\n",
        "end\n"
      ],
      "metadata": {
        "id": "4CkaNRtt_8pB",
        "outputId": "b2eb49ac-a776-489e-c490-4dd239d399e1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "add_envelope_constraints (generic function with 2 methods)"
            ]
          },
          "metadata": {},
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# if you have multiple extreme points\n",
        "new_icnn_lp_list = Array{JuMP.Model}(undef, length(extreme_points))\n",
        "\n",
        "for i in 1:length(extreme_points)\n",
        "    extreme_points_i = extreme_points[i]\n",
        "    new_icnn_lp = add_envelope_constraints(filepath, extreme_points_i, icnn_lp)\n",
        "    new_icnn_lp_list[i] = new_icnn_lp\n",
        "    print(new_icnn_lp)\n",
        "end\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "tyQUoOLPmNAD",
        "outputId": "3f60175b-2838-4e28-e076-0225be3bbf5d"
      },
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/latex": "$$ \\begin{aligned}\n\\min\\quad & output\\_var\\\\\n\\text{Subject to} \\quad & -input\\_var + {\\_}_{3} = 0\\\\\n & output\\_var - {\\_}_{6} = 0\\\\\n & input\\_var + 3 a_{1} = 0\\\\\n & input\\_var \\geq -3\\\\\n & {\\_}_{4} \\geq 0\\\\\n & {\\_}_{5} \\geq 0\\\\\n & 2.0587143898010254 {\\_}_{3} + {\\_}_{4} \\geq -0.9489541053771973\\\\\n & -1.120605707168579 {\\_}_{3} + {\\_}_{5} \\geq 2.0486631393432617\\\\\n & 2.0735292434692383 {\\_}_{3} - 0.667317271232605 {\\_}_{4} - 1.5244076251983643 {\\_}_{5} + {\\_}_{6} \\geq -2.1556038856506348\\\\\n & input\\_var \\leq 0\\\\\n & output\\_var - 7.5531774 a_{1} - 0.9673938 a_{2} \\leq 0\\\\\n & input\\_var = 0\\\\\n & a_{1} \\geq 0\\\\\n & a_{2} \\geq 0\\\\\n\\end{aligned} $$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n",
            "Warning: -/+Inf bounds detected on at least 5 variables. Initializing with values -/+1.0e6. This may affect global optimal values and run times.\n",
            "\n",
            "\u001b[0m*** Alpine ended with status OPTIMAL ***\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/latex": "$$ \\begin{aligned}\n\\min\\quad & output\\_var\\\\\n\\text{Subject to} \\quad & -input\\_var + {\\_}_{3} = 0\\\\\n & output\\_var - {\\_}_{6} = 0\\\\\n & input\\_var - 3 a_{2} = 0\\\\\n & input\\_var \\geq 0\\\\\n & {\\_}_{4} \\geq 0\\\\\n & {\\_}_{5} \\geq 0\\\\\n & 2.0587143898010254 {\\_}_{3} + {\\_}_{4} \\geq -0.9489541053771973\\\\\n & -1.120605707168579 {\\_}_{3} + {\\_}_{5} \\geq 2.0486631393432617\\\\\n & 2.0735292434692383 {\\_}_{3} - 0.667317271232605 {\\_}_{4} - 1.5244076251983643 {\\_}_{5} + {\\_}_{6} \\geq -2.1556038856506348\\\\\n & input\\_var \\leq 3\\\\\n & output\\_var - 0.9673938 a_{1} + 0.1284143 a_{2} \\leq 0\\\\\n & input\\_var = 3\\\\\n & a_{1} \\geq 0\\\\\n & a_{2} \\geq 0\\\\\n\\end{aligned} $$"
          },
          "metadata": {}
        }
      ]
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    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "J5Bs-SjPmNwo"
      },
      "execution_count": 9,
      "outputs": []
    }
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