{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## My First Robust Problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We consider a simple linear optimization problem with an ellipsoidal uncertainty set. (TODO complete)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cvxpy as cp\n",
    "import numpy as np\n",
    "import lropt as lr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 2\n",
    "P = np.array([[1.,2],[1.,0.]])\n",
    "A = np.eye(2)\n",
    "b = np.zeros(2)\n",
    "c = np.array([2,1])\n",
    "a = np.array([.4,0.5])\n",
    "\n",
    "u = lr.UncertainParameter(n,\n",
    "                          uncertainty_set=lr.Ellipsoidal(A=A, b=b))\n",
    "\n",
    "x = cp.Variable(n)\n",
    "\n",
    "objective = cp.Minimize(c @ x)\n",
    "constraints = [(P @ u + a) @ x <= 10]\n",
    "\n",
    "prob = lr.RobustProblem(objective, constraints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimal value =  -20.76298271930384\n",
      "optimal solution =  [ -1.83921308 -17.08455655]\n"
     ]
    }
   ],
   "source": [
    "prob.solve()\n",
    "\n",
    "print(\"optimal value = \", objective.value)\n",
    "print(\"optimal solution = \", x.value)\n"
   ]
  }
 ],
 "metadata": {
  "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": "3.11.3"
  },
  "vscode": {
   "interpreter": {
    "hash": "e3ed6dde042e78d86e091991aef4e6276872e8fbcb7e1edcb6e9eacd7157f213"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}