{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization with CSDL_alpha models\n",
    "\n",
    "*Problem:*\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\underset{x, y \\in \\mathbb{R}}{\\text{minimize}} & \\quad x^4 + y^4 \\\\\n",
    "\\text{subject to} & \\quad x\\geq0, \\\\\n",
    "                  & \\quad x+y=1, \\\\\n",
    "                  & \\quad x-y\\geq1.\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/modopt/modopt/external_libraries/snopt/snoptc.py:6: UserWarning: snoptc from 'optimize' could not be imported\n",
      "  warnings.warn(\"snoptc from 'optimize' could not be imported\")\n",
      "/Users/modopt/modopt/external_libraries/snopt/snoptc.py:10: UserWarning: snopt7_python from 'optimize.solvers' could not be imported\n",
      "  warnings.warn(\"snopt7_python from 'optimize.solvers' could not be imported\")\n",
      "/Users/modopt/modopt/external_libraries/snopt/snopt_optimizer.py:6: UserWarning: SNOPT_options from 'optimize' could not be imported\n",
      "  warnings.warn(\"SNOPT_options from 'optimize' could not be imported\")\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Directory  quartic_outputs  already exists\n",
      "Computing gradient >>>>>>>>>>\n",
      "---------Computed gradient---------\n",
      "Computing Jacobian >>>>>>>>>>\n",
      "---------Computed Jacobian---------\n",
      "Computing objective >>>>>>>>>>\n",
      "---------Computed objective---------\n",
      "Computing constraints >>>>>>>>>>\n",
      "---------Computed constraints---------\n",
      "Computing objective >>>>>>>>>>\n",
      "---------Computed objective---------\n",
      "Computing constraints >>>>>>>>>>\n",
      "---------Computed constraints---------\n",
      "Computing objective >>>>>>>>>>\n",
      "---------Computed objective---------\n",
      "Computing constraints >>>>>>>>>>\n",
      "---------Computed constraints---------\n",
      "\n",
      "----------------------------------------------------------------------------\n",
      "Derivative type | Calc norm  | FD norm    | Abs error norm | Rel error norm \n",
      "----------------------------------------------------------------------------\n",
      "\n",
      "Gradient        | 2.0100e+01 | 2.0100e+01 | 3.0000e-05     | 1.4925e-06    \n",
      "Jacobian        | 1.4213e+00 | 1.4213e+00 | 2.8262e-10     | 1.9885e-10    \n",
      "----------------------------------------------------------------------------\n",
      "\n",
      "Computing constraints >>>>>>>>>>\n",
      "---------Computed constraints---------\n",
      "Computing constraints >>>>>>>>>>\n",
      "---------Computed constraints---------\n",
      "Computing objective >>>>>>>>>>\n",
      "---------Computed objective---------\n",
      "Computing gradient >>>>>>>>>>\n",
      "---------Computed gradient---------\n",
      "Computing constraints >>>>>>>>>>\n",
      "---------Computed constraints---------\n",
      "Computing constraints >>>>>>>>>>\n",
      "---------Computed constraints---------\n",
      "Computing Jacobian >>>>>>>>>>\n",
      "---------Computed Jacobian---------\n",
      "Computing Jacobian >>>>>>>>>>\n",
      "---------Computed Jacobian---------\n",
      "Computing objective >>>>>>>>>>\n",
      "---------Computed objective---------\n",
      "Computing constraints >>>>>>>>>>\n",
      "---------Computed constraints---------\n",
      "Computing constraints >>>>>>>>>>\n",
      "---------Computed constraints---------\n",
      "Computing gradient >>>>>>>>>>\n",
      "---------Computed gradient---------\n",
      "Computing Jacobian >>>>>>>>>>\n",
      "---------Computed Jacobian---------\n",
      "Computing Jacobian >>>>>>>>>>\n",
      "---------Computed Jacobian---------\n",
      "\n",
      " \t ==============\n",
      "\t Scipy summary:\n",
      "\t ==============\n",
      "\t Problem                    : quartic\n",
      "\t Solver                     : scipy_slsqp\n",
      "\t Success                    : True\n",
      "\t Message                    : Optimization terminated successfully\n",
      "\t Objective                  : 5.0000000000003375\n",
      "\t Gradient norm              : 20.000000000001013\n",
      "\t Total time                 : 0.004601955413818359\n",
      "\t Major iterations           : 2\n",
      "\t Total function evals       : 2\n",
      "\t Total gradient evals       : 2\n",
      "\t ==================================================\n"
     ]
    }
   ],
   "source": [
    "import csdl_alpha as csdl\n",
    "\n",
    "# minimize x^4 + y^4 subject to x>=0, x+y=1, x-y>=1.\n",
    "\n",
    "rec = csdl.Recorder()\n",
    "rec.start()\n",
    "\n",
    "# add design variables\n",
    "x = csdl.Variable(name = 'x', value=1.)\n",
    "y = csdl.Variable(name = 'y', value=1.)\n",
    "x.set_as_design_variable(lower = 0.0)\n",
    "y.set_as_design_variable(scaler=10.)\n",
    "\n",
    "# add objective\n",
    "z = x**4 + y**4\n",
    "z.add_name('z')\n",
    "z.set_as_objective(scaler=5.0)\n",
    "\n",
    "# add constraints\n",
    "constraint_1 = x + y\n",
    "constraint_2 = x - y\n",
    "constraint_1.add_name('constraint_1')\n",
    "constraint_2.add_name('constraint_2')\n",
    "constraint_1.set_as_constraint(lower=1., upper=1.)\n",
    "constraint_2.set_as_constraint(lower=1.)\n",
    "\n",
    "rec.stop()\n",
    "\n",
    "# Create a Simulator object from the Recorder object\n",
    "sim = csdl.experimental.PySimulator(rec)\n",
    "\n",
    "# Import CSDLAlphaProblem from modopt\n",
    "from modopt import CSDLAlphaProblem\n",
    "\n",
    "# Instantiate your problem using the csdl Simulator object and name your problem\n",
    "prob = CSDLAlphaProblem(problem_name='quartic',simulator=sim)\n",
    "\n",
    "# Import your preferred optimizer from modopt\n",
    "from modopt import SQP, SLSQP, SNOPT\n",
    "\n",
    "# Setup your preferred optimizer (here, SLSQP) with the Problem object \n",
    "# Pass in the options for your chosen optimizer\n",
    "optimizer = SLSQP(prob, solver_options={'maxiter':20, 'ftol':1e-6})\n",
    "# optimizer = SQP(prob, maxiter=20)\n",
    "snopt_options = {\n",
    "    'Infinite bound': 1.0e20, \n",
    "    'Verify level': 3,\n",
    "    'Verbose': True\n",
    "    }\n",
    "# optimizer = SNOPT(prob, solver_options=snopt_options)\n",
    "\n",
    "# Check first derivatives at the initial guess, if needed\n",
    "optimizer.check_first_derivatives(prob.x0)\n",
    "\n",
    "# Solve your optimization problem\n",
    "optimizer.solve()\n",
    "\n",
    "# Print the results of optimization\n",
    "optimizer.print_results()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}