authors/gomfy/ampl-lecture/intro_to_optimization.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zL3HGBXASh_7"
      },
      "source": [
        "# Introduction to Mathematical Optimization\n",
        "[![intro_to_optimization.ipynb](https://img.shields.io/badge/github-%23121011.svg?logo=github)](https://github.com/ampl/colab.ampl.com/blob/master/authors/gomfy/ampl-lecture/intro_to_optimization.ipynb) [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ampl/colab.ampl.com/blob/master/authors/gomfy/ampl-lecture/intro_to_optimization.ipynb) [![Kaggle](https://kaggle.com/static/images/open-in-kaggle.svg)](https://kaggle.com/kernels/welcome?src=https://github.com/ampl/colab.ampl.com/blob/master/authors/gomfy/ampl-lecture/intro_to_optimization.ipynb) [![Gradient](https://assets.paperspace.io/img/gradient-badge.svg)](https://console.paperspace.com/github/ampl/colab.ampl.com/blob/master/authors/gomfy/ampl-lecture/intro_to_optimization.ipynb) [![Open In SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ampl/colab.ampl.com/blob/master/authors/gomfy/ampl-lecture/intro_to_optimization.ipynb) [![Hits](https://h.ampl.com/https://github.com/ampl/colab.ampl.com/blob/master/authors/gomfy/ampl-lecture/intro_to_optimization.ipynb)](https://colab.ampl.com)\n",
        "\n",
        "Description: Basic introduction to optimization and AMPL via unconstrained optimization\n",
        "\n",
        "Tags: ampl-lecture, amplpy, ampl, introduction, optimization, convexity, unconstrained\n",
        "\n",
        "Notebook author: Gyorgy Matyasfalvi <<gyorgy@ampl.com>>\n",
        "\n",
        "References:\n",
        "\n",
        "* AMPL a Modeling Language for Mathematical Programming -- Robert Fourer et al.\n",
        "* Linear Programming (Foundations and Extensions) -- Robert J. Vanderbei\n",
        "* Introduction to Linear Optimization -- Dimitris Bertsimas et al.\n",
        "* Convex Analysis and Optimization -- Dimitri P. Bertsekas et al."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4zzXBeylSh_9",
        "outputId": "c4b82268-dd8f-46c9-9eee-45f7a4ddc3a2"
      },
      "outputs": [],
      "source": [
        "# Install dependencies\n",
        "%pip install -q amplpy pandas numpy matplotlib"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 84,
          "referenced_widgets": [
            "c9cc3c7cdecb457c82537a8724db27dd",
            "44fb3da9600445618ead73d1a40db103",
            "c722945202c4406a91c550de63b490db",
            "cd99bcabd8714a1d8837774dce2d56fa",
            "a232aa9b0cf246e7940f70881433c186",
            "524ec7b4130846f08c437d2f391fb298",
            "4a2eb8e3c39b41c2aacc0af8b9ad49ed",
            "e034623cac3c4b92a49633a10ff15d54",
            "5e149ed4232047798311ccf131e793c9",
            "24c388b0341546c494e789399789d3a8",
            "87bfdfa6670a4b2c92324ab23c456c89",
            "e24d5c9859c3496491fdc5f0c0705f66",
            "707221eee0514c3d99e96325e340aba1"
          ]
        },
        "id": "6s3dvpaTSh__",
        "outputId": "fe537364-82c9-43e1-8d14-5561ceb01e33"
      },
      "outputs": [],
      "source": [
        "# Google Colab & Kaggle integration\n",
        "from amplpy import AMPL, ampl_notebook\n",
        "\n",
        "ampl = ampl_notebook(\n",
        "    modules=[\"open\", \"gurobi\"],  # modules to install\n",
        "    license_uuid=\"default\",  # license to use\n",
        ")  # instantiate AMPL object and register magics"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "KzKC65-6Sh__"
      },
      "outputs": [],
      "source": [
        "# Import all necessary libraries\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from math import log, cos, sin, pi, sqrt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ahz85TBQSh__"
      },
      "source": [
        "## Problem types\n",
        "An optimization problem, in its most general form, can be expressed as follows:\n",
        "$\n",
        "\\begin{equation}\n",
        "\\begin{array}{lll}\n",
        "&\\min           & f(x)  &    \\\\\n",
        "&\\textrm{s.t.}  & x  \\in \\Omega,\n",
        "\\end{array} \\tag{1}\n",
        "\\end{equation}\n",
        "$\n",
        "In this equation, $ f: \\mathbb{R}^n \\rightarrow \\mathbb{R} $ and $ \\Omega \\subset \\mathbb{R}^n $.\n",
        "We refer to $ f $ as the *objective function*, $ x \\in \\Omega $ as the *constraints*, and the vector $ x $ as the *decision variables*.\n",
        "A vector $x \\in \\mathbb{R}^n$ satisfying all of the constraints (i.e. $x \\in \\mathbb{\\Omega}$) is called a *feasible solution*.\n",
        "A feasible solution $x^*$ that minimizes the objective function is called an *optimal feasible solution*, or simply, an *optimal solution*.\n",
        "\n",
        "If $ \\Omega $ is equal to $ \\mathbb{R}^n $, we are dealing with an unconstrained optimization problem. These are **significantly easier** to solve compared to constrained optimization problems.\n",
        "\n",
        "In our exploration of optimization problems, it's crucial to understand the nature of functions and constraints.\n",
        "We need to distinguish between convex and non-convex problems, as well as between linear and non-linear ones.\n",
        "While our primary focus in this training is on linear constrained optimization problems, we will initially delve into some non-linear and non-convex challenges to elucidate key concepts.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fAMrUSaYSiAA"
      },
      "source": [
        "## Convex problems\n",
        "Convex problems, particularly those that are smooth, are preferred for two main reasons:\n",
        "1. They provide a guarantee of **global optimality**.\n",
        "2. There are many efficient algorithms (implemented in various solvers) available for solving these problems.\n",
        "\n",
        "A problem defined by the above equation (1) is considered convex if $ f $ is a convex function and $ \\Omega $ is a nonempty closed convex set.\n",
        "\n",
        "### Definition of convexity\n",
        "**Convex set**: A subset $\\Omega$ of $\\mathbb{R}^n$ is called *convex* if\n",
        "$\n",
        "\\begin{equation}\n",
        "\\lambda x + (1-\\lambda) y \\in \\Omega \\qquad \\forall x,y \\in \\Omega, \\quad \\forall \\lambda \\in [0,1]. \\tag{2}\n",
        "\\end{equation}\n",
        "$\n",
        "\n",
        "**Geometrically**, the line segment connecting $x$ to $y$ must also lie within the set $\\Omega$.\n",
        "\n",
        "\n",
        "<br>\n",
        "<br>\n",
        "\n",
        "**Convex function**: Let $\\Omega$ be a convex subset of $\\mathbb{R}^n$. A function $\\Omega : \\mathbb{R}^n \\rightarrow \\mathbb{R}$ is convex if we have\n",
        "\n",
        "$\n",
        "\\begin{equation}\n",
        "f(\\lambda x + (1-\\lambda) y) \\leq \\lambda f(x) + (1-\\lambda) f(y) \\qquad \\forall x,y \\in \\Omega, \\quad \\forall \\lambda \\in [0,1]. \\tag{3}\n",
        "\\end{equation}\n",
        "$\n",
        "\n",
        "**Geometrically**, the line segment connecting $(x, f (x))$ to $(y, f (y))$ must sit above the graph of $f$.\n",
        "\n",
        "**Also geometrically**, a function is convex if and only if the area above its graph is convex."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "kbUom7mySiAA",
        "outputId": "f84ae80b-b7fb-46da-e606-3c8963534e65"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Plot convex functions\n",
        "\n",
        "\n",
        "# Define the functions\n",
        "def easy(x):\n",
        "    return x**2\n",
        "\n",
        "\n",
        "def not_so_easy(x):\n",
        "    return (x - 1) ** 2 + x\n",
        "\n",
        "\n",
        "# Generate x values\n",
        "x = np.linspace(-4, 4, 400)\n",
        "\n",
        "# Generate y values\n",
        "ye = easy(x)\n",
        "yne = not_so_easy(x)\n",
        "\n",
        "# Create the plot\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(x, ye, label=\"easy: y = x^2\")\n",
        "plt.plot(x, yne, label=\"not_so_easy: y = (x-1)^2 + x\")\n",
        "\n",
        "# Add a line that connects two points\n",
        "x_not_so_easy = [-3, 3]\n",
        "y_not_so_easy = [not_so_easy(-3), not_so_easy(3)]\n",
        "plt.plot(\n",
        "    x_not_so_easy,\n",
        "    y_not_so_easy,\n",
        "    color=\"orange\",\n",
        "    linestyle=\"--\",\n",
        "    label=\"convex comb of (-3, not_so_easy(-3)) and (3, not_so_easy(3))\",\n",
        ")\n",
        "x_easy = [-2, 2]\n",
        "y_easy = [easy(-2), easy(2)]\n",
        "plt.plot(\n",
        "    x_easy,\n",
        "    y_easy,\n",
        "    color=\"blue\",\n",
        "    linestyle=\"--\",\n",
        "    label=\"convex comb of (-2, easy(-2)) and (2, easy(2))\",\n",
        ")\n",
        "\n",
        "\n",
        "plt.title(\"Convex functions: easy and not_so_easy\")\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S7GlcvpHSiAB"
      },
      "source": [
        "### Where/what is the minimum of the easy function? ;-)\n",
        "\n",
        "### How about the not-so-easy function?\n",
        "\n",
        "### Let's ask AMPL!"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_j_dy3jMSiAB",
        "outputId": "41f426b8-a7f9-4b6c-970a-962ac7e5af8a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Error executing \"solve\" command:\n",
            "No solver specified:  option solver is ''.\n"
          ]
        }
      ],
      "source": [
        "%%ampl_eval\n",
        "reset; reset option;                # reset AMPL, this is needed for when we run the cell multiple times,\n",
        "                                    # AMPL complains about redeclaration of entities.\n",
        "var x;                              # Declare our variable\n",
        "minimize not_so_easy: (x-1)^2 + x;  # Define our objective function\n",
        "solve;                              # Attempt to solve"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SgywFRelSiAB"
      },
      "source": [
        "**Whoops!!! We always need to specify the solver before attempting to solve!**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M7iwaRavSiAC",
        "outputId": "9130c5ea-b936-478d-e1e2-c0e2a0776bc9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Ipopt 3.12.13: \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 http://projects.coin-or.org/Ipopt\n",
            "******************************************************************************\n",
            "\n",
            "This is Ipopt version 3.12.13, running with linear solver mumps.\n",
            "NOTE: Other linear solvers might be more efficient (see Ipopt documentation).\n",
            "\n",
            "Number of nonzeros in equality constraint Jacobian...:        0\n",
            "Number of nonzeros in inequality constraint Jacobian.:        0\n",
            "Number of nonzeros in Lagrangian Hessian.............:        1\n",
            "\n",
            "Total number of variables............................:        1\n",
            "                     variables with only lower bounds:        0\n",
            "                variables with lower and upper bounds:        0\n",
            "                     variables with only upper bounds:        0\n",
            "Total number of equality constraints.................:        0\n",
            "Total number of inequality constraints...............:        0\n",
            "        inequality constraints with only lower bounds:        0\n",
            "   inequality constraints with lower and upper bounds:        0\n",
            "        inequality constraints with only upper bounds:        0\n",
            "\n",
            "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
            "   0  1.0000000e+00 0.00e+00 1.00e+00  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0\n",
            "   1  7.5000000e-01 0.00e+00 0.00e+00  -1.7 5.00e-01    -  1.00e+00 1.00e+00f  1\n",
            "\n",
            "Number of Iterations....: 1\n",
            "\n",
            "                                   (scaled)                 (unscaled)\n",
            "Objective...............:   7.5000000000000000e-01    7.5000000000000000e-01\n",
            "Dual infeasibility......:   0.0000000000000000e+00    0.0000000000000000e+00\n",
            "Constraint violation....:   0.0000000000000000e+00    0.0000000000000000e+00\n",
            "Complementarity.........:   0.0000000000000000e+00    0.0000000000000000e+00\n",
            "Overall NLP error.......:   0.0000000000000000e+00    0.0000000000000000e+00\n",
            "\n",
            "\n",
            "Number of objective function evaluations             = 2\n",
            "Number of objective gradient evaluations             = 2\n",
            "Number of equality constraint evaluations            = 0\n",
            "Number of inequality constraint evaluations          = 0\n",
            "Number of equality constraint Jacobian evaluations   = 0\n",
            "Number of inequality constraint Jacobian evaluations = 0\n",
            "Number of Lagrangian Hessian evaluations             = 1\n",
            "Total CPU secs in IPOPT (w/o function evaluations)   =      0.001\n",
            "Total CPU secs in NLP function evaluations           =      0.000\n",
            "\n",
            "EXIT: Optimal Solution Found.\n",
            "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b \n",
            "Ipopt 3.12.13: Optimal Solution Found\n",
            "\n",
            "suffix ipopt_zU_out OUT;\n",
            "suffix ipopt_zL_out OUT;\n",
            "\n",
            "Optimum: ( 0.5 0.75 )\n"
          ]
        }
      ],
      "source": [
        "%%ampl_eval\n",
        "option solver ipopt;                        # Use Ipopt as our solver\n",
        "solve;                                      # Issue solve command and send the problem, this time, to Ipopt\n",
        "                                            # After succesful completion of solve AMPL retrieves the solutions from Ipopt\n",
        "print;                                      # Add a new line (only for formatting purposes)\n",
        "print \"Optimum: (\", x, not_so_easy, \")\";    # Let's also print the solution!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O25zzBD1SiAC"
      },
      "source": [
        "### Let's try a more difficult case"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "nbEVzRsOSiAC",
        "outputId": "cb783283-25f0-408f-b331-48652024de3f"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Draw a difficult to optimize convex function\n",
        "\n",
        "\n",
        "# Define the function\n",
        "def difficult(x):\n",
        "    return (x - 1) ** 2 - log(x + 1)\n",
        "\n",
        "\n",
        "# Generate x values\n",
        "x = np.linspace(-0.9999, 10, 400)\n",
        "\n",
        "# Generate y values\n",
        "y = [difficult(i) for i in x]\n",
        "\n",
        "# Create the plot\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(x, y, label=\"y = (x-1)^2 - log(x+1)\")\n",
        "\n",
        "# Add a line that connects two points\n",
        "x_difficult = [-0.5, 6]\n",
        "y_difficult = [difficult(-0.5), difficult(6)]\n",
        "plt.plot(\n",
        "    x_difficult,\n",
        "    y_difficult,\n",
        "    color=\"blue\",\n",
        "    linestyle=\"--\",\n",
        "    label=\"convex comb of (-0.5, difficult(-0.5)) and (6, difficult(6))\",\n",
        ")\n",
        "\n",
        "plt.title(\"Convex function: difficult\")\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uNXsyy1GSiAC"
      },
      "source": [
        "### How do we know function `difficult` is convex?\n",
        "1. We can apply the definition.\n",
        "2. We can examine the epigraph of the function (or in this simple case just look at the graph of the function) and make conclusions based off of that.\n",
        "3. Also, if we know that $x^2$ and $-\\log(x)$ are convex then there are some powerful theorems we can use to help us recognize convex functions:\n",
        "\n",
        "**Sum of convex functions is convex:** Let $f_i: \\mathbb{R}^n \\rightarrow \\mathbb{R}$, $i = 1,\\ldots,m$, let $\\lambda_1, \\ldots, \\lambda_m$ be positive scalars, and consider the function $g: \\mathbb{R}^n \\rightarrow \\mathbb{R}$ given by:\n",
        "\n",
        "$\n",
        "\\begin{equation}\n",
        "g(x) = \\lambda_1 f_1(x) + \\ldots + \\lambda_m f_m(x).\\tag{4}\n",
        "\\end{equation}\n",
        "$\n",
        "\n",
        "If $f_1, \\ldots, f_m$ are convex, then $g$ is also convex.\n",
        "\n",
        "\n",
        "**Transformations preserving convexity of domain:** Let $f: \\mathbb{R}^m \\rightarrow \\mathbb{R}$ be a given function, let $A \\in \\mathbb{R}^{m \\times n}$ matrix, and consider the function $g: \\mathbb{R}^n \\rightarrow \\mathbb{R}$ given by:\n",
        "\n",
        "$\n",
        "\\begin{equation}\n",
        "g(x) = f(Ax).\\tag{5}\n",
        "\\end{equation}\n",
        "$\n",
        "\n",
        "If $f$ is convex, then $g$ is also convex (e.g norm functions are convex and so are least squares type problems, e.g. $\\min_{x \\in \\mathbb{R}^n} || Ax -b||^2_2$).\n",
        "\n",
        "**Maximum of convex functions is convex:** Let $f_i: \\mathbb{R}^n \\rightarrow \\mathbb{R}$, $i \\in I$, where $I$ is an arbitrary index set, and consider the function $g: \\mathbb{R}^n \\rightarrow \\mathbb{R}$ given by:\n",
        "\n",
        "$\n",
        "\\begin{equation}\n",
        "g(x) = \\max_{i \\in I} f_i(x). \\tag{6}\n",
        "\\end{equation}\n",
        "$\n",
        "\n",
        "If $f_i, \\; i \\in I$, are convex, then $g$ is also convex."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cmcsn7U-SiAC"
      },
      "source": [
        "## Let's get ready for our first exercise with some basic AMPL syntax\n",
        "More details later (or in the [AMPL book](https://ampl.com/learn/ampl-book/), or just ask ;-)\n",
        "\n",
        "### Variable declarations\n",
        "To declare our variables in AMPL, we first use the `var` keyword followed by the variable name, optional attributes, and a semicolon.\n",
        "It is also worth mentioning that by default, AMPL initializes all variables to zero unless an initial value is provided via an attribute (e.g. `var x := 1;` in which case the initial value of `x` becomes 1).\n",
        "This will be important to keep in mind later on when we discuss computing the value of expressions that involve variables.\n",
        "\n",
        "**Reminder:** Each AMPL statement ends with a semicolon.\n",
        "\n",
        "### Objective declarations\n",
        "To specify an objective function in AMPL, we first have to specify the direction of optimization via the keywords `maximize` or `minimize`, which is followed by a name, a colon, an expression involving our variables, and a semicolon.\n",
        "\n",
        "**Reminder:** Variables must be declared before they can be used in an expression.\n",
        "\n",
        "It's good practice to use a descriptive name for the objective function, such as `profit`, which reflects what we're trying to optimize.\n",
        "In the next example you might choose to use the `difficult` qualifier.\n",
        "The expression should be a mathematical formula involving our variables that reflect the goal of the optimization problem."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AQyePLsFSiAD"
      },
      "source": [
        "# EXERCISE 1\n",
        "1. Create a code cell below.\n",
        "\n",
        "2. Start with the magic: `%%ampl_eval`\n",
        "\n",
        "3. Reset the state of the AMPL interpreter with `reset;` and `reset option;`.\n",
        "\n",
        "4. Then use the AMPL keywords `var` and `minimize`, as well as the built-in function `log()` to formulate the model that minimizes `difficult()` (the built-in AMPL function `log()` is base $e$ just like the Python function `log()`).\n",
        "\n",
        "5. Compute the minimum using the `ipopt` solver.\n",
        "\n",
        "6. Then print the solution using AMPL's `print` command."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SMOoYTSzSiAD"
      },
      "source": [
        "## SOLUTION"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "y60qHucSSiAD",
        "outputId": "a55828ca-2d4c-4250-e184-cb018a6f8e2a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Ipopt 3.12.13: \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 http://projects.coin-or.org/Ipopt\n",
            "******************************************************************************\n",
            "\n",
            "This is Ipopt version 3.12.13, running with linear solver mumps.\n",
            "NOTE: Other linear solvers might be more efficient (see Ipopt documentation).\n",
            "\n",
            "Number of nonzeros in equality constraint Jacobian...:        0\n",
            "Number of nonzeros in inequality constraint Jacobian.:        0\n",
            "Number of nonzeros in Lagrangian Hessian.............:        1\n",
            "\n",
            "Total number of variables............................:        1\n",
            "                     variables with only lower bounds:        0\n",
            "                variables with lower and upper bounds:        0\n",
            "                     variables with only upper bounds:        0\n",
            "Total number of equality constraints.................:        0\n",
            "Total number of inequality constraints...............:        0\n",
            "        inequality constraints with only lower bounds:        0\n",
            "   inequality constraints with lower and upper bounds:        0\n",
            "        inequality constraints with only upper bounds:        0\n",
            "\n",
            "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
            "   0  1.0000000e+00 0.00e+00 3.00e+00  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0\n",
            "   1 -6.9314718e-01 0.00e+00 5.00e-01  -1.0 1.00e+00    -  1.00e+00 1.00e+00f  1\n",
            "   2 -7.4912498e-01 0.00e+00 5.56e-03  -1.7 2.22e-01    -  1.00e+00 1.00e+00f  1\n",
            "   3 -7.4913199e-01 0.00e+00 5.79e-07  -3.8 2.52e-03    -  1.00e+00 1.00e+00f  1\n",
            "   4 -7.4913199e-01 0.00e+00 6.11e-15  -8.6 2.63e-07    -  1.00e+00 1.00e+00f  1\n",
            "\n",
            "Number of Iterations....: 4\n",
            "\n",
            "                                   (scaled)                 (unscaled)\n",
            "Objective...............:  -7.4913198728379427e-01   -7.4913198728379427e-01\n",
            "Dual infeasibility......:   6.1062266354383610e-15    6.1062266354383610e-15\n",
            "Constraint violation....:   0.0000000000000000e+00    0.0000000000000000e+00\n",
            "Complementarity.........:   0.0000000000000000e+00    0.0000000000000000e+00\n",
            "Overall NLP error.......:   6.1062266354383610e-15    6.1062266354383610e-15\n",
            "\n",
            "\n",
            "Number of objective function evaluations             = 5\n",
            "Number of objective gradient evaluations             = 5\n",
            "Number of equality constraint evaluations            = 0\n",
            "Number of inequality constraint evaluations          = 0\n",
            "Number of equality constraint Jacobian evaluations   = 0\n",
            "Number of inequality constraint Jacobian evaluations = 0\n",
            "Number of Lagrangian Hessian evaluations             = 4\n",
            "Total CPU secs in IPOPT (w/o function evaluations)   =      0.004\n",
            "Total CPU secs in NLP function evaluations           =      0.000\n",
            "\n",
            "EXIT: Optimal Solution Found.\n",
            "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b \n",
            "Ipopt 3.12.13: Optimal Solution Found\n",
            "\n",
            "suffix ipopt_zU_out OUT;\n",
            "suffix ipopt_zL_out OUT;\n",
            "\n",
            "Optimum: ( 1.2247448713915863 -0.7491319872837943 )\n"
          ]
        }
      ],
      "source": [
        "%%ampl_eval\n",
        "reset; reset option;                # reset AMPL, this is needed for when we run the cell multiple times,\n",
        "                                    # AMPL complains about redeclaration of entities.\n",
        "var x;                              # Declare our variable\n",
        "minimize difficult: (x-1)^2 - log(x+1);  # Define our objective function\n",
        "option solver ipopt;                # Use Ipopt as our solver\n",
        "solve;                              # Attempt to solve\n",
        "print;                              # Add a new line (only for formatting purposes)\n",
        "print \"Optimum: (\", x, difficult, \")\";    # Let's also print the solution!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7zBR83H-SiAD"
      },
      "source": [
        "## Non-convex functions\n",
        "We've consistently found the optimal solution without much difficulty.\n",
        "This is expected since we've been dealing with convex smooth functions.\n",
        "Local non-linear solvers like Ipopt are well-equipped for these types of problems.\n",
        "Now, let's examine a non-convex function and observe the outcome."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "9ZRIe3j3SiAD",
        "outputId": "90b9196d-88c1-4456-eef0-46df6368f5a9"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Draw a non-convex function\n",
        "\n",
        "\n",
        "# Define the function\n",
        "def non_convex(x):\n",
        "    return 1 + (x - 2) ** 2 - cos(2 * pi * x)\n",
        "\n",
        "\n",
        "# Generate x values\n",
        "x = np.linspace(-1, 5, 400)\n",
        "\n",
        "# Generate y values\n",
        "y = [non_convex(i) for i in x]\n",
        "\n",
        "# Create the plot\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(x, y, label=\"y = 1 + (x-2)^2 - cos(2*pi*x)\")\n",
        "\n",
        "# Add a line that connects two points\n",
        "x_non_convex = [0, 3]\n",
        "y_non_convex = [non_convex(0), non_convex(3)]\n",
        "plt.plot(\n",
        "    x_non_convex,\n",
        "    y_non_convex,\n",
        "    color=\"red\",\n",
        "    linestyle=\"--\",\n",
        "    label=\"convex comb of (0, non_convex(0)) and (3, non_convex(3))\",\n",
        ")\n",
        "\n",
        "plt.title(\"Non-convex function: non_convex\")\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RmIg2rBgSiAD"
      },
      "source": [
        "## For the second exercise you will need a new AMPL entity called a parameter\n",
        "\n",
        "### Parameter declarations\n",
        "For the second exercise, we will declare $\\pi$ as a parameter in AMPL.\n",
        "To do this, we use the keyword `param`, followed by the parameter name. While assigning an initial is generally optional, in this instance we provide one.\n",
        "The declaration is then concluded with a semi-colon."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0qyRC12-SiAE"
      },
      "source": [
        "# EXERCISE 2\n",
        "1. Create a code cell below.\n",
        "\n",
        "2. Start with the magic: `%%ampl_eval`\n",
        "\n",
        "3. Reset the state of the AMPL interpreter with `reset;` and `reset option;`.\n",
        "\n",
        "4. Then use the following parameter definition: `param pi = 4 * atan(1);` to declare $\\pi$.\n",
        "\n",
        "5. Next, use keywords `var` and `minimize`, as well as the built-in function `cos()` to formulate the model that minimizes `non_convex()`.\n",
        "\n",
        "5. Compute the minimum using the `ipopt` solver.\n",
        "\n",
        "6. Then print the solution using AMPL's `print` command."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0w0hN_SISiAE"
      },
      "source": [
        "## SOLUTION"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XrnYBFPBSiAE",
        "outputId": "644431d3-1cad-469c-a6c5-62f8d8658d42"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Ipopt 3.12.13: \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 http://projects.coin-or.org/Ipopt\n",
            "******************************************************************************\n",
            "\n",
            "This is Ipopt version 3.12.13, running with linear solver mumps.\n",
            "NOTE: Other linear solvers might be more efficient (see Ipopt documentation).\n",
            "\n",
            "Number of nonzeros in equality constraint Jacobian...:        0\n",
            "Number of nonzeros in inequality constraint Jacobian.:        0\n",
            "Number of nonzeros in Lagrangian Hessian.............:        1\n",
            "\n",
            "Total number of variables............................:        1\n",
            "                     variables with only lower bounds:        0\n",
            "                variables with lower and upper bounds:        0\n",
            "                     variables with only upper bounds:        0\n",
            "Total number of equality constraints.................:        0\n",
            "Total number of inequality constraints...............:        0\n",
            "        inequality constraints with only lower bounds:        0\n",
            "   inequality constraints with lower and upper bounds:        0\n",
            "        inequality constraints with only upper bounds:        0\n",
            "\n",
            "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
            "   0  4.0000000e+00 0.00e+00 4.00e+00  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0\n",
            "   1  3.8015805e+00 0.00e+00 2.29e-01  -1.0 9.64e-02    -  1.00e+00 1.00e+00f  1\n",
            "   2  3.8008142e+00 0.00e+00 3.18e-03  -1.7 6.64e-03    -  1.00e+00 1.00e+00f  1\n",
            "   3  3.8008141e+00 0.00e+00 6.73e-07  -3.8 9.48e-05    -  1.00e+00 1.00e+00f  1\n",
            "   4  3.8008141e+00 0.00e+00 3.02e-14  -8.6 2.01e-08    -  1.00e+00 1.00e+00f  1\n",
            "\n",
            "Number of Iterations....: 4\n",
            "\n",
            "                                   (scaled)                 (unscaled)\n",
            "Objective...............:   3.8008140784160975e+00    3.8008140784160975e+00\n",
            "Dual infeasibility......:   3.0198066269804258e-14    3.0198066269804258e-14\n",
            "Constraint violation....:   0.0000000000000000e+00    0.0000000000000000e+00\n",
            "Complementarity.........:   0.0000000000000000e+00    0.0000000000000000e+00\n",
            "Overall NLP error.......:   3.0198066269804258e-14    3.0198066269804258e-14\n",
            "\n",
            "\n",
            "Number of objective function evaluations             = 5\n",
            "Number of objective gradient evaluations             = 5\n",
            "Number of equality constraint evaluations            = 0\n",
            "Number of inequality constraint evaluations          = 0\n",
            "Number of equality constraint Jacobian evaluations   = 0\n",
            "Number of inequality constraint Jacobian evaluations = 0\n",
            "Number of Lagrangian Hessian evaluations             = 4\n",
            "Total CPU secs in IPOPT (w/o function evaluations)   =      0.004\n",
            "Total CPU secs in NLP function evaluations           =      0.000\n",
            "\n",
            "EXIT: Optimal Solution Found.\n",
            "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b \n",
            "Ipopt 3.12.13: Optimal Solution Found\n",
            "\n",
            "suffix ipopt_zU_out OUT;\n",
            "suffix ipopt_zL_out OUT;\n",
            "\n",
            "Optimum: ( 0.1031696971029012 3.8008140784160975 )\n"
          ]
        }
      ],
      "source": [
        "%%ampl_eval\n",
        "reset; reset option;                # reset AMPL, this is needed for when we run the cell multiple times,\n",
        "                                    # AMPL complains about redeclaration of entities.\n",
        "param pi = 4 * atan(1);             # Define pi\n",
        "var x;                              # Declare our variable\n",
        "minimize non_convex: 1 + (x-2)^2 - cos(2*pi*x);  # Define our objective function\n",
        "option solver ipopt;                # Use Ipopt as our solver\n",
        "solve;                              # Attempt to solve\n",
        "print;                              # Add a new line (only for formatting purposes)\n",
        "print \"Optimum: (\", x, non_convex, \")\";    # Let's also print the solution!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8uSFSFvzSiAE"
      },
      "source": [
        "## Did we find the optimum?\n",
        "Let's check by plotting the results."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "2h9cjwIsSiAE",
        "outputId": "38a62efe-fabe-4b2e-e796-1b14a0e76f0b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Ipopt 3.12.13: \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 http://projects.coin-or.org/Ipopt\n",
            "******************************************************************************\n",
            "\n",
            "This is Ipopt version 3.12.13, running with linear solver mumps.\n",
            "NOTE: Other linear solvers might be more efficient (see Ipopt documentation).\n",
            "\n",
            "Number of nonzeros in equality constraint Jacobian...:        0\n",
            "Number of nonzeros in inequality constraint Jacobian.:        0\n",
            "Number of nonzeros in Lagrangian Hessian.............:        1\n",
            "\n",
            "Total number of variables............................:        1\n",
            "                     variables with only lower bounds:        0\n",
            "                variables with lower and upper bounds:        0\n",
            "                     variables with only upper bounds:        0\n",
            "Total number of equality constraints.................:        0\n",
            "Total number of inequality constraints...............:        0\n",
            "        inequality constraints with only lower bounds:        0\n",
            "   inequality constraints with lower and upper bounds:        0\n",
            "        inequality constraints with only upper bounds:        0\n",
            "\n",
            "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
            "   0  4.0000000e+00 0.00e+00 4.00e+00  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0\n",
            "   1  3.8015805e+00 0.00e+00 2.29e-01  -1.0 9.64e-02    -  1.00e+00 1.00e+00f  1\n",
            "   2  3.8008142e+00 0.00e+00 3.18e-03  -1.7 6.64e-03    -  1.00e+00 1.00e+00f  1\n",
            "   3  3.8008141e+00 0.00e+00 6.73e-07  -3.8 9.48e-05    -  1.00e+00 1.00e+00f  1\n",
            "   4  3.8008141e+00 0.00e+00 3.02e-14  -8.6 2.01e-08    -  1.00e+00 1.00e+00f  1\n",
            "\n",
            "Number of Iterations....: 4\n",
            "\n",
            "                                   (scaled)                 (unscaled)\n",
            "Objective...............:   3.8008140784160975e+00    3.8008140784160975e+00\n",
            "Dual infeasibility......:   3.0198066269804258e-14    3.0198066269804258e-14\n",
            "Constraint violation....:   0.0000000000000000e+00    0.0000000000000000e+00\n",
            "Complementarity.........:   0.0000000000000000e+00    0.0000000000000000e+00\n",
            "Overall NLP error.......:   3.0198066269804258e-14    3.0198066269804258e-14\n",
            "\n",
            "\n",
            "Number of objective function evaluations             = 5\n",
            "Number of objective gradient evaluations             = 5\n",
            "Number of equality constraint evaluations            = 0\n",
            "Number of inequality constraint evaluations          = 0\n",
            "Number of equality constraint Jacobian evaluations   = 0\n",
            "Number of inequality constraint Jacobian evaluations = 0\n",
            "Number of Lagrangian Hessian evaluations             = 4\n",
            "Total CPU secs in IPOPT (w/o function evaluations)   =      0.003\n",
            "Total CPU secs in NLP function evaluations           =      0.000\n",
            "\n",
            "EXIT: Optimal Solution Found.\n",
            "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b \n",
            "Ipopt 3.12.13: Optimal Solution Found\n",
            "\n",
            "suffix ipopt_zU_out OUT;\n",
            "suffix ipopt_zL_out OUT;\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Now instead of using magic cells we will be using the AMPL API directly\n",
        "ampl = AMPL()  # Instantiate an AMPL object\n",
        "ampl.reset()  # Reset AMPL\n",
        "# Load the model\n",
        "ampl.eval(\n",
        "    r\"\"\"\n",
        "    var x;\n",
        "    param pi = 4 * atan(1);\n",
        "    minimize non_convex: 1 + (x-2)^2 - cos(2*pi*x);\n",
        "    \"\"\"\n",
        ")\n",
        "ampl.option[\"solver\"] = \"ipopt\"  # Use Ipopt as our solver\n",
        "ampl.solve()  # Solve the problem with Ipopt\n",
        "sol_df = ampl.get_data(\n",
        "    \"x, non_convex\"\n",
        ").to_pandas()  # Retrieve the solution (we can retrieve x and non_convex because they are indexed over the same set).\n",
        "\n",
        "\n",
        "# Define the function\n",
        "def non_convex(x):\n",
        "    return 1 + (x - 2) ** 2 - cos(2 * pi * x)\n",
        "\n",
        "\n",
        "# Generate x values\n",
        "x = np.linspace(-1, 5, 400)\n",
        "\n",
        "# Generate y values\n",
        "y = [non_convex(i) for i in x]\n",
        "\n",
        "# Create the plot\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(x, y, label=\"y = 1 + (x-2)^2 - cos(2*pi*x)\")\n",
        "\n",
        "# Plot the values in sol_df\n",
        "plt.scatter(\n",
        "    sol_df[\"x\"], sol_df[\"non_convex\"], color=\"red\", s=100, label=\"solution point\"\n",
        ")\n",
        "\n",
        "plt.title(\"Non-convex function: non_convex\")\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CWT4iRzqSiAE"
      },
      "source": [
        "## As expected we only found a local optimum\n",
        "To address this, let's switch to a global solver.\n",
        "Global solvers excel at managing non-convex functions characterized by multiple local optima.\n",
        "In situations where pinpointing the global optimum is crucial, these solvers come into their own.\n",
        "However, it's worth noting that they typically operate at a slower speeds compared to local solvers."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hO6lIQ1dSiAF"
      },
      "source": [
        "# EXERCISE 3\n",
        "1. Go back to the previous code cell and change the solver to `gurobi`, then re-run the cell.\n",
        "\n",
        "2. What happens if you change the default starting value of `x := 0` to `x := 1.5`?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BUPd1somSiAF"
      },
      "source": [
        "## SOLUTION"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 633
        },
        "id": "c5CBICSTSiAF",
        "outputId": "442e56f1-65cd-4ecf-f8e1-161a3905a559"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Gurobi 11.0.0: \b\b\b\b\b\b\b\b\b\b\b\b\b\b\bGurobi 11.0.0: optimal solution; objective 0.0001245693477\n",
            "21 simplex iterations\n",
            "1 branching nodes\n",
            " \n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Now instead of using magic cells we will be using the AMPL API directly\n",
        "ampl = AMPL()  # Instantiate an AMPL object\n",
        "ampl.reset()  # Reset AMPL\n",
        "# Load the model\n",
        "ampl.eval(\n",
        "    r\"\"\"\n",
        "    var x;\n",
        "    param pi = 4 * atan(1);\n",
        "    minimize non_convex: 1 + (x-2)^2 - cos(2*pi*x);\n",
        "    \"\"\"\n",
        ")\n",
        "ampl.option[\"solver\"] = \"gurobi\"  # THIS TIME use Gurobi as our solver\n",
        "ampl.solve()  # Solve the problem with Gurobi\n",
        "sol_df = ampl.get_data(\n",
        "    \"x, non_convex\"\n",
        ").to_pandas()  # Retrieve the solution (we can retrieve x and non_convex because they are indexed over the same set).\n",
        "\n",
        "\n",
        "# Define the function\n",
        "def non_convex(x):\n",
        "    return 1 + (x - 2) ** 2 - cos(2 * pi * x)\n",
        "\n",
        "\n",
        "# Generate x values\n",
        "x = np.linspace(-1, 5, 400)\n",
        "\n",
        "# Generate y values\n",
        "y = [non_convex(i) for i in x]\n",
        "\n",
        "# Create the plot\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(x, y, label=\"y = 1 + (x-2)^2 - cos(2*pi*x)\")\n",
        "\n",
        "# Plot the values in sol_df\n",
        "plt.scatter(\n",
        "    sol_df[\"x\"], sol_df[\"non_convex\"], color=\"red\", s=100, label=\"solution point\"\n",
        ")\n",
        "\n",
        "plt.title(\"Non-convex function: non_convex\")\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "G-2021LsSiAF",
        "outputId": "3fed3b6b-f4ff-4ec0-93a1-5139a2644be2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Ipopt 3.12.13: \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 http://projects.coin-or.org/Ipopt\n",
            "******************************************************************************\n",
            "\n",
            "This is Ipopt version 3.12.13, running with linear solver mumps.\n",
            "NOTE: Other linear solvers might be more efficient (see Ipopt documentation).\n",
            "\n",
            "Number of nonzeros in equality constraint Jacobian...:        0\n",
            "Number of nonzeros in inequality constraint Jacobian.:        0\n",
            "Number of nonzeros in Lagrangian Hessian.............:        1\n",
            "\n",
            "Total number of variables............................:        1\n",
            "                     variables with only lower bounds:        0\n",
            "                variables with lower and upper bounds:        0\n",
            "                     variables with only upper bounds:        0\n",
            "Total number of equality constraints.................:        0\n",
            "Total number of inequality constraints...............:        0\n",
            "        inequality constraints with only lower bounds:        0\n",
            "   inequality constraints with lower and upper bounds:        0\n",
            "        inequality constraints with only upper bounds:        0\n",
            "\n",
            "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
            "   0  2.2500000e+00 0.00e+00 1.00e+00  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0\n",
            "   1  2.2292158e+00 0.00e+00 1.60e+00  -1.7 1.60e-02   2.0 1.00e+00 1.00e+00f  1\n",
            "   2  2.2171747e+00 0.00e+00 1.86e+00  -1.7 6.97e-03   2.4 1.00e+00 1.00e+00f  1\n",
            "   3  2.1271626e+00 0.00e+00 3.15e+00  -1.7 3.58e-02   1.9 1.00e+00 1.00e+00f  1\n",
            "   4  2.0738808e+00 0.00e+00 3.68e+00  -1.7 1.56e-02   2.4 1.00e+00 1.00e+00f  1\n",
            "   5  1.6820191e+00 0.00e+00 5.88e+00  -1.7 8.05e-02   1.9 1.00e+00 1.00e+00f  1\n",
            "   6  3.6130577e-01 0.00e+00 5.01e+00  -1.7 9.62e-01   1.4 1.00e+00 5.00e-01f  2\n",
            "   7  3.8708552e-02 0.00e+00 1.78e+00  -1.7 1.79e-01    -  1.00e+00 1.00e+00f  1\n",
            "   8  2.2782440e-05 0.00e+00 4.35e-02  -1.7 4.44e-02    -  1.00e+00 1.00e+00f  1\n",
            "   9  4.3157924e-15 0.00e+00 5.98e-07  -2.5 1.05e-03    -  1.00e+00 1.00e+00f  1\n",
            "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
            "  10  0.0000000e+00 0.00e+00 3.08e-15  -8.6 1.44e-08    -  1.00e+00 1.00e+00f  1\n",
            "\n",
            "Number of Iterations....: 10\n",
            "\n",
            "                                   (scaled)                 (unscaled)\n",
            "Objective...............:   0.0000000000000000e+00    0.0000000000000000e+00\n",
            "Dual infeasibility......:   3.0778731099548636e-15    3.0778731099548636e-15\n",
            "Constraint violation....:   0.0000000000000000e+00    0.0000000000000000e+00\n",
            "Complementarity.........:   0.0000000000000000e+00    0.0000000000000000e+00\n",
            "Overall NLP error.......:   3.0778731099548636e-15    3.0778731099548636e-15\n",
            "\n",
            "\n",
            "Number of objective function evaluations             = 16\n",
            "Number of objective gradient evaluations             = 11\n",
            "Number of equality constraint evaluations            = 0\n",
            "Number of inequality constraint evaluations          = 0\n",
            "Number of equality constraint Jacobian evaluations   = 0\n",
            "Number of inequality constraint Jacobian evaluations = 0\n",
            "Number of Lagrangian Hessian evaluations             = 10\n",
            "Total CPU secs in IPOPT (w/o function evaluations)   =      0.010\n",
            "Total CPU secs in NLP function evaluations           =      0.000\n",
            "\n",
            "EXIT: Optimal Solution Found.\n",
            "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b \n",
            "Ipopt 3.12.13: Optimal Solution Found\n",
            "\n",
            "suffix ipopt_zU_out OUT;\n",
            "suffix ipopt_zL_out OUT;\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Now instead of using magic cells we will be using the AMPL API directly\n",
        "ampl = AMPL()  # Instantiate an AMPL object\n",
        "ampl.reset()  # Reset AMPL\n",
        "# Load the model\n",
        "ampl.eval(\n",
        "    r\"\"\"\n",
        "    var x := 1.5;                                             # Give x an initial value other than 0 (AMPL's default is 0)\n",
        "    param pi = 4 * atan(1);\n",
        "    minimize non_convex: 1 + (x-2)^2 - cos(2*pi*x);\n",
        "    \"\"\"\n",
        ")\n",
        "ampl.option[\"solver\"] = \"ipopt\"  # Use Ipopt as our solver\n",
        "ampl.solve()  # Solve the problem with Ipopt\n",
        "sol_df = ampl.get_data(\n",
        "    \"x, non_convex\"\n",
        ").to_pandas()  # Retrieve the solution (we can retrieve x and non_convex because they are indexed over the same set).\n",
        "\n",
        "\n",
        "# Define the function\n",
        "def non_convex(x):\n",
        "    return 1 + (x - 2) ** 2 - cos(2 * pi * x)\n",
        "\n",
        "\n",
        "# Generate x values\n",
        "x = np.linspace(-1, 5, 400)\n",
        "\n",
        "# Generate y values\n",
        "y = [non_convex(i) for i in x]\n",
        "\n",
        "# Create the plot\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(x, y, label=\"y = 1 + (x-2)^2 - cos(2*pi*x)\")\n",
        "\n",
        "# Plot the values in sol_df\n",
        "plt.scatter(\n",
        "    sol_df[\"x\"], sol_df[\"non_convex\"], color=\"red\", s=100, label=\"solution point\"\n",
        ")\n",
        "\n",
        "plt.title(\"Non-convex function: non_convex\")\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ToHovFtVSiAF"
      },
      "source": [
        "# EXERCISE 4\n",
        "1. Let's return to our difficult function and try solving it with another solver called `highs`. Did we find the optimum?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "suZJ3V5uSiAF"
      },
      "source": [
        "## SOLUTION"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2ERDx2yCSiAG",
        "outputId": "a42c1d95-dcd7-48a9-9b1e-2be2775fea88"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "HiGHS 1.6.0: \n",
            "------------ WARNINGS ------------\n",
            "WARNING:  \"PLApprox\"\n",
            "  An expression of type 'LogConstraint' has been\n",
            "piecewise-linearly approximated. Set cvt:plapprox:reltol\n",
            "to control precision (currently 0.010000).\n",
            "WARNING:  \"PLApproxDomain\"\n",
            "  Argument domain of a 'LogConstraint'\n",
            "has been reduced to [0.000001, 1000000.000000] for numerical reasons\n",
            "(partially controlled by cvt:plapprox:domain.)\n",
            "\b\b\b\b\b\b\b\b\b\b\b\b\b------------ WARNINGS ------------\n",
            "WARNING:  \"PLApprox\"\n",
            "  An expression of type 'LogConstraint' has been\n",
            "piecewise-linearly approximated. Set cvt:plapprox:reltol\n",
            "to control precision (currently 0.010000).\n",
            "WARNING:  \"PLApproxDomain\"\n",
            "  Argument domain of a 'LogConstraint'\n",
            "has been reduced to [0.000001, 1000000.000000] for numerical reasons\n",
            "(partially controlled by cvt:plapprox:domain.)\n",
            "  Error -1 for call Highs_run(lp())\n"
          ]
        }
      ],
      "source": [
        "ampl = AMPL()  # Instantiate an AMPL object\n",
        "ampl.eval(\n",
        "    r\"\"\"\n",
        "            var x;                                              # Declare our variable\n",
        "            minimize difficult: (x-1)^2 - log(x+1);             # Define our objective function\n",
        "          \"\"\"\n",
        ")\n",
        "\n",
        "ampl.option[\"solver\"] = \"highs\"  # Select the solver\n",
        "ampl.solve()  # Attempt to solve"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lW_aN8FMSiAG"
      },
      "source": [
        "HiGHS is a solver adept at tackling Mixed Integer Programming (MIP) and Quadratic Programming (QP) problems, which means it can efficiently handle linear programming, integer programming, and quadratic programming challenges.\n",
        "However, it encounters limitations with our objective function, which includes a logarithmic term.\n",
        "\n",
        "\n",
        "As HiGHS cannot directly process the logarithmic element, the MP solver driver compensates by approximating this term using piecewise linear functions.\n",
        "The WARNING message you encountered is to alert you that such an approximation has been applied.\n",
        "\n",
        "\n",
        "The term 'LogConstraint' might seem misleading. This stems from AMPL's bookkeeping method where the objective function is treated as the 0th constraint. Despite the approximation, HiGHS is unable to minimize our function and consequently returns an error."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GkbSQsebSiAG"
      },
      "source": [
        "## Programmatically checking the solve result status\n",
        "The following code segment demonstrates how to verify programmatically whether a satisfactory solution has been attained."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "e9X6UWosSiAG",
        "outputId": "92c6b32d-2e1a-4970-f03f-ec1f8d4f2271"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "HiGHS 1.6.0: \n",
            "------------ WARNINGS ------------\n",
            "WARNING:  \"PLApprox\"\n",
            "  An expression of type 'LogConstraint' has been\n",
            "piecewise-linearly approximated. Set cvt:plapprox:reltol\n",
            "to control precision (currently 0.010000).\n",
            "WARNING:  \"PLApproxDomain\"\n",
            "  Argument domain of a 'LogConstraint'\n",
            "has been reduced to [0.000001, 1000000.000000] for numerical reasons\n",
            "(partially controlled by cvt:plapprox:domain.)\n",
            "\b\b\b\b\b\b\b\b\b\b\b\b\b------------ WARNINGS ------------\n",
            "WARNING:  \"PLApprox\"\n",
            "  An expression of type 'LogConstraint' has been\n",
            "piecewise-linearly approximated. Set cvt:plapprox:reltol\n",
            "to control precision (currently 0.010000).\n",
            "WARNING:  \"PLApproxDomain\"\n",
            "  Argument domain of a 'LogConstraint'\n",
            "has been reduced to [0.000001, 1000000.000000] for numerical reasons\n",
            "(partially controlled by cvt:plapprox:domain.)\n",
            "  Error -1 for call Highs_run(lp())\n",
            "\n",
            "0\tsolved\n",
            "100\tsolved?\n",
            "200\tinfeasible\n",
            "300\tunbounded\n",
            "400\tlimit\n",
            "500\tfailure\n",
            "\n",
            "Warning: Problem not solved to optimality!\n",
            "\t solve_result_num = 500\n"
          ]
        }
      ],
      "source": [
        "ampl = AMPL()  # Instantiate an AMPL object\n",
        "ampl.eval(\n",
        "    r\"\"\"\n",
        "            var x;                                              # Declare our variable\n",
        "            minimize difficult: (x-1)^2 - log(x+1);             # Define our objective function\n",
        "          \"\"\"\n",
        ")\n",
        "\n",
        "ampl.option[\"solver\"] = \"highs\"  # Select the solver\n",
        "ampl.solve()  # Attempt to solve\n",
        "print(\n",
        "    ampl.option[\"solve_result_table\"]\n",
        ")  # Print the solve result table, this will inform us of the various solution codes.\n",
        "result_df = ampl.get_data(\"solve_result_num\").to_pandas()  # Retrieve solution status\n",
        "# Check if the problem was solved if not print warning\n",
        "srn = result_df[\"solve_result_num\"].iloc[0]\n",
        "if srn != 0:\n",
        "    print(f\"Warning: Problem not solved to optimality!\\n\\t solve_result_num = {srn}\")"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.10.12"
    },
    "vscode": {
      "interpreter": {
        "hash": "ee4198aac13dae9b6fccd443041680d99c2643c4956ef7c80ff6dcc0057cb523"
      }
    },
    "widgets": {
      "application/vnd.jupyter.widget-state+json": {
        "c9cc3c7cdecb457c82537a8724db27dd": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "VBoxModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "VBoxModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "VBoxView",
            "box_style": "",
            "children": [
              "IPY_MODEL_44fb3da9600445618ead73d1a40db103",
              "IPY_MODEL_c722945202c4406a91c550de63b490db",
              "IPY_MODEL_cd99bcabd8714a1d8837774dce2d56fa",
              "IPY_MODEL_a232aa9b0cf246e7940f70881433c186"
            ],
            "layout": "IPY_MODEL_524ec7b4130846f08c437d2f391fb298"
          }
        },
        "44fb3da9600445618ead73d1a40db103": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "model_module_version": "1.0.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_model_name": "OutputModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/output",
            "_view_module_version": "1.0.0",
            "_view_name": "OutputView",
            "layout": "IPY_MODEL_87bfdfa6670a4b2c92324ab23c456c89",
            "msg_id": "",
            "outputs": [
              {
                "output_type": "stream",
                "name": "stdout",
                "text": [
                  "AMPL License UUID (you can use free https://ampl.com/ce or https://ampl.com/courses licenses):\n"
                ]
              }
            ]
          }
        },
        "c722945202c4406a91c550de63b490db": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "HBoxModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "HBoxModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "HBoxView",
            "box_style": "",
            "children": [
              "IPY_MODEL_4a2eb8e3c39b41c2aacc0af8b9ad49ed"
            ],
            "layout": "IPY_MODEL_e034623cac3c4b92a49633a10ff15d54"
          }
        },
        "cd99bcabd8714a1d8837774dce2d56fa": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "model_module_version": "1.0.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_model_name": "OutputModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/output",
            "_view_module_version": "1.0.0",
            "_view_name": "OutputView",
            "layout": "IPY_MODEL_e24d5c9859c3496491fdc5f0c0705f66",
            "msg_id": "",
            "outputs": []
          }
        },
        "a232aa9b0cf246e7940f70881433c186": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "model_module_version": "1.0.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_model_name": "OutputModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/output",
            "_view_module_version": "1.0.0",
            "_view_name": "OutputView",
            "layout": "IPY_MODEL_707221eee0514c3d99e96325e340aba1",
            "msg_id": "",
            "outputs": [
              {
                "output_type": "stream",
                "name": "stdout",
                "text": [
                  "Licensed to AMPL Community Edition License for the AMPL Model Colaboratory (https://colab.ampl.com).\n"
                ]
              }
            ]
          }
        },
        "524ec7b4130846f08c437d2f391fb298": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "4a2eb8e3c39b41c2aacc0af8b9ad49ed": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "TextModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "TextModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "TextView",
            "continuous_update": true,
            "description": "License UUID:",
            "description_tooltip": null,
            "disabled": false,
            "layout": "IPY_MODEL_5e149ed4232047798311ccf131e793c9",
            "placeholder": "​",
            "style": "IPY_MODEL_24c388b0341546c494e789399789d3a8",
            "value": ""
          }
        },
        "e034623cac3c4b92a49633a10ff15d54": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "5e149ed4232047798311ccf131e793c9": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "24c388b0341546c494e789399789d3a8": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "DescriptionStyleModel",
          "model_module_version": "1.5.0",
          "state": {
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "DescriptionStyleModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "StyleView",
            "description_width": "initial"
          }
        },
        "87bfdfa6670a4b2c92324ab23c456c89": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "e24d5c9859c3496491fdc5f0c0705f66": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "707221eee0514c3d99e96325e340aba1": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        }
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}