notebooks/LP example 2.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 2: illustrating degenerate and unbounded cases"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Utility function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve(solver='ipopt'):\n",
    "    # Solve the problem\n",
    "    opt = SolverFactory(solver)\n",
    "    opt.solve(model)\n",
    "\n",
    "    # Get the solution\n",
    "    print(\"x[1] = %.2f\" % model.x[1].value)\n",
    "    print(\"x[2] = %.2f\" % model.x[2].value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyomo.environ import *\n",
    "\n",
    "# Instantiate the problem\n",
    "model = ConcreteModel()\n",
    "\n",
    "# Create the variables\n",
    "model.x = Var([1, 2], domain=NonNegativeReals)\n",
    "\n",
    "# Create the constraints\n",
    "model.Constraint1 = Constraint(expr=-model.x[1] + model.x[2] <= 1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Vary the objective"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unique solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x[1] = 0.00\n",
      "x[2] = 0.00\n"
     ]
    }
   ],
   "source": [
    "model.OBJ = Objective(expr=model.x[1] + model.x[2])       # (0, 0) unique\n",
    "solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Another unique solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: Implicitly replacing the Component attribute OBJ (type=<class\n",
      "    'pyomo.core.base.objective.SimpleObjective'>) on block unknown with a new\n",
      "    Component (type=<class 'pyomo.core.base.objective.SimpleObjective'>). This\n",
      "    is usually indicative of a modelling error. To avoid this warning, use\n",
      "    block.del_component() and block.add_component().\n",
      "x[1] = 0.00\n",
      "x[2] = 1.00\n"
     ]
    }
   ],
   "source": [
    "model.OBJ = Objective(expr=model.x[1] - 0.5 * model.x[2])  # (0, 1) unique\n",
    "solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Several solutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: Implicitly replacing the Component attribute OBJ (type=<class\n",
      "    'pyomo.core.base.objective.SimpleObjective'>) on block unknown with a new\n",
      "    Component (type=<class 'pyomo.core.base.objective.SimpleObjective'>). This\n",
      "    is usually indicative of a modelling error. To avoid this warning, use\n",
      "    block.del_component() and block.add_component().\n",
      "x[1] = 0.00\n",
      "x[2] = 0.00\n"
     ]
    }
   ],
   "source": [
    "model.OBJ = Objective(expr=model.x[1])                    # Degenerate\n",
    "solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unbounded"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: Implicitly replacing the Component attribute OBJ (type=<class\n",
      "    'pyomo.core.base.objective.SimpleObjective'>) on block unknown with a new\n",
      "    Component (type=<class 'pyomo.core.base.objective.SimpleObjective'>). This\n",
      "    is usually indicative of a modelling error. To avoid this warning, use\n",
      "    block.del_component() and block.add_component().\n",
      "WARNING: Loading a SolverResults object with a warning status into\n",
      "    model=unknown;\n",
      "        message from solver=Ipopt 3.12.8\\x3a Iterates diverging; problem might\n",
      "        be unbounded.\n",
      "x[1] = 0.00\n",
      "x[2] = 0.00\n"
     ]
    }
   ],
   "source": [
    "# Pay attention that, although the problem is unbounded, there may still be values from an older run ...\n",
    "model.OBJ = Objective(sense=maximize, expr=model.x[1] + model.x[2]) # Unbounded\n",
    "solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Several solutions / unbounded (border case)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: Implicitly replacing the Component attribute OBJ (type=<class\n",
      "    'pyomo.core.base.objective.SimpleObjective'>) on block unknown with a new\n",
      "    Component (type=<class 'pyomo.core.base.objective.SimpleObjective'>). This\n",
      "    is usually indicative of a modelling error. To avoid this warning, use\n",
      "    block.del_component() and block.add_component().\n",
      "x[1] = 7.38\n",
      "x[2] = 8.38\n"
     ]
    }
   ],
   "source": [
    "# Observe how the solution varies...\n",
    "model.OBJ = Objective(expr=model.x[1] - model.x[2])       # Degenerate / unbounded\n",
    "solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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