Pyomo Differentiate Example

pyomo_differentiate_example_incorrect.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import symbols, diff\n",
    "from sympy.utilities.lambdify import lambdify\n",
    "\n",
    "from pyomo.environ import ConcreteModel, PercentFraction, Var, Objective, Constraint\n",
    "from pyomo.opt import SolverFactory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example Problem\n",
    "\n",
    "\\begin{align}\n",
    "max: 3 x_1 + x_2 \\\\\n",
    "s.t. y = x_1^2 + x_2^2 \\\\\n",
    "y \\leq 0.5 \\\\\n",
    "\\frac{\\partial y}{\\partial x_1} \\leq \\frac{1}{2} \\\\\n",
    "x_1 \\in [0, 1] \\\\\n",
    "x_2 \\in [0, 1] \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve(model):\n",
    "    solver = 'ipopt'\n",
    "    solver_io = 'nl'\n",
    "    opt = SolverFactory(solver, solver_io=solver_io)\n",
    "    opt.solve(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sympy Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.4114378434226194,\n",
       " 0.2500000040426455,\n",
       " 0.2500000040426455,\n",
       " 0.5000000066862389)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_1, x_2 = symbols('x_1 x_2')\n",
    "y = x_1 ** 2 + x_2 **2\n",
    "\n",
    "model = ConcreteModel()\n",
    "\n",
    "model.x = Var([0, 1], domain=PercentFraction)\n",
    "model.y = Var([0])\n",
    "\n",
    "model.OBJ = Objective(expr=3 * model.x[0] + model.x[1], sense=-1)\n",
    "model.Constraint1 = Constraint(expr=model.y[0] == model.x[0] ** 2 + model.x[1] ** 2)\n",
    "model.Constraint2 = Constraint(expr=model.y[0] <= 0.5)\n",
    "model.Constraint3 = Constraint(expr=lambdify(x_1, diff(y, x_1))(model.x[0]) <= 0.5)\n",
    "\n",
    "solve(model)\n",
    "model.OBJ(), model.x[0].value, model.x[0].value, model.y[0].value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Differentiate Implementation (incorrect)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyomo.core.expr import differentiate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ERROR: Constructing component 'Constraint3' from data=None failed: ValueError:\n",
      "    Invalid constraint expression. The constraint expression resolved to a\n",
      "    trivial Boolean (True) instead of a Pyomo object. Please modify your rule\n",
      "    to return Constraint.Feasible instead of True.\n",
      "\n",
      "    Error thrown for Constraint 'Constraint3'\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "Invalid constraint expression. The constraint expression resolved to a trivial Boolean (True) instead of a Pyomo object. Please modify your rule to return Constraint.Feasible instead of True.\n\nError thrown for Constraint 'Constraint3'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-5-dfd202bbbaf6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mConstraint1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mConstraint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mConstraint2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mConstraint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m0.5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mConstraint3\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mConstraint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdifferentiate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mConstraint1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbody\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwrt\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m0.5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0msolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/work/miniconda3/envs/py37/lib/python3.7/site-packages/pyomo/core/base/block.py\u001b[0m in \u001b[0;36m__setattr__\u001b[0;34m(self, name, val)\u001b[0m\n\u001b[1;32m    568\u001b[0m                 \u001b[0;31m# Pyomo components are added with the add_component method.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    569\u001b[0m                 \u001b[0;31m#\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 570\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_component\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mval\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    571\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    572\u001b[0m                 \u001b[0;31m#\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/work/miniconda3/envs/py37/lib/python3.7/site-packages/pyomo/core/base/block.py\u001b[0m in \u001b[0;36madd_component\u001b[0;34m(self, name, val)\u001b[0m\n\u001b[1;32m   1008\u001b[0m                              _blockName, str(data))\n\u001b[1;32m   1009\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1010\u001b[0;31m                 \u001b[0mval\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconstruct\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1011\u001b[0m             \u001b[0;32mexcept\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1012\u001b[0m                 \u001b[0merr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexc_info\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/work/miniconda3/envs/py37/lib/python3.7/site-packages/pyomo/core/base/constraint.py\u001b[0m in \u001b[0;36mconstruct\u001b[0;34m(self, data)\u001b[0m\n\u001b[1;32m    763\u001b[0m                            err))\n\u001b[1;32m    764\u001b[0m                     \u001b[0;32mraise\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 765\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_setitem_when_not_present\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtmp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    766\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    767\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/work/miniconda3/envs/py37/lib/python3.7/site-packages/pyomo/core/base/constraint.py\u001b[0m in \u001b[0;36m_setitem_when_not_present\u001b[0;34m(self, index, value)\u001b[0m\n\u001b[1;32m    712\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    713\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_setitem_when_not_present\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 714\u001b[0;31m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_check_skip_add\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    715\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    716\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/work/miniconda3/envs/py37/lib/python3.7/site-packages/pyomo/core/base/constraint.py\u001b[0m in \u001b[0;36m_check_skip_add\u001b[0;34m(self, index, expr)\u001b[0m\n\u001b[1;32m    889\u001b[0m                        \u001b[0mexpr\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;34m\"Feasible\"\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0;34m\"Infeasible\"\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    890\u001b[0m                        \u001b[0mexpr\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 891\u001b[0;31m                        _get_indexed_component_data_name(self,index)))\n\u001b[0m\u001b[1;32m    892\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    893\u001b[0m         \u001b[0;31m#\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: Invalid constraint expression. The constraint expression resolved to a trivial Boolean (True) instead of a Pyomo object. Please modify your rule to return Constraint.Feasible instead of True.\n\nError thrown for Constraint 'Constraint3'"
     ]
    }
   ],
   "source": [
    "model = ConcreteModel()\n",
    "\n",
    "model.x = Var([0, 1], domain=PercentFraction, initialize=0.3)\n",
    "model.y = Var([0], domain=PercentFraction, initialize=0.4)\n",
    "\n",
    "model.OBJ = Objective(expr=3 * model.x[0] + model.x[1], sense=-1)\n",
    "model.Constraint1 = Constraint(expr=model.y[0] == model.x[0] ** 2 + model.x[1] ** 2)\n",
    "model.Constraint2 = Constraint(expr=model.y[0] <= 0.5)\n",
    "model.Constraint3 = Constraint(expr=differentiate(model.Constraint1.body, wrt=model.x[0]) <= 0.5)\n",
    "\n",
    "solve(model)\n",
    "model.OBJ(), model.x[0].value, model.x[1].value, model.y[0].value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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