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Nonlinear Programming Using CppAD and Ipopt: Example and Test
Purpose
This example program demonstrates how to use ipopt_solve to solve the example problem in the Ipopt documentation; i.e., the problem minimize x 1 * x 4 * ( x 1 + x 2 + x 3 ) + x 3 subject to x 1 * x 2 * x 3 * x 4 ≥ 25 x 1 2 + x 2 2 + x 3 2 + x 4 2 = 40 1 ≤ x 1 , x 2 , x 3 , x 4 ≤ 5
Configuration Requirement
This example will be compiled and tested provided that ipopt_prefix is specified on the cmake command line. `

    # include <cppad/ipopt/solve.hpp>

    namespace {
         using CppAD::AD;

         class FG_eval {
         public:
              typedef CPPAD_TESTVECTOR( AD<double> ) ADvector;
              void operator()(ADvector& fg, const ADvector& x)
              {     assert( fg.size() == 3 );
                   assert( x.size()  == 4 );

                   // Fortran style indexing
                   AD<double> x1 = x[0];
                   AD<double> x2 = x[1];
                   AD<double> x3 = x[2];
                   AD<double> x4 = x[3];
                   // f(x)
                   fg[0] = x1 * x4 * (x1 + x2 + x3) + x3;
                   // g_1 (x)
                   fg[1] = x1 * x2 * x3 * x4;
                   // g_2 (x)
                   fg[2] = x1 * x1 + x2 * x2 + x3 * x3 + x4 * x4;
                   //
                   return;
              }
         };
    }

    bool get_started(void)
    {     bool ok = true;
         size_t i;
         typedef CPPAD_TESTVECTOR( double ) Dvector;

         // number of independent variables (domain dimension for f and g)
         size_t nx = 4;
         // number of constraints (range dimension for g)
         size_t ng = 2;
         // initial value of the independent variables
         Dvector xi(nx);
         xi[0] = 1.0;
         xi[1] = 5.0;
         xi[2] = 5.0;
         xi[3] = 1.0;
         // lower and upper limits for x
         Dvector xl(nx), xu(nx);
         for(i = 0; i < nx; i++)
         {     xl[i] = 1.0;
              xu[i] = 5.0;
         }
         // lower and upper limits for g
         Dvector gl(ng), gu(ng);
         gl[0] = 25.0;     gu[0] = 1.0e19;
         gl[1] = 40.0;     gu[1] = 40.0;

         // object that computes objective and constraints
         FG_eval fg_eval;

         // options
         std::string options;
         // turn off any printing
         options += "Integer print_level  0\n";
         options += "String  sb           yes\n";
         // maximum number of iterations
         options += "Integer max_iter     10\n";
         // approximate accuracy in first order necessary conditions;
         // see Mathematical Programming, Volume 106, Number 1,
         // Pages 25-57, Equation (6)
         options += "Numeric tol          1e-6\n";
         // derivative testing
         options += "String  derivative_test            second-order\n";
         // maximum amount of random pertubation; e.g.,
         // when evaluation finite diff
         options += "Numeric point_perturbation_radius  0.\n";

         // place to return solution
         CppAD::ipopt::solve_result<Dvector> solution;

         // solve the problem
         CppAD::ipopt::solve<Dvector, FG_eval>(
              options, xi, xl, xu, gl, gu, fg_eval, solution
         );
         //
         // Check some of the solution values
         //
         ok &= solution.status == CppAD::ipopt::solve_result<Dvector>::success;
         //
         double check_x[]  = { 1.000000, 4.743000, 3.82115, 1.379408 };
         double check_zl[] = { 1.087871, 0.,       0.,      0.       };
         double check_zu[] = { 0.,       0.,       0.,      0.       };
         double rel_tol    = 1e-6;  // relative tolerance
         double abs_tol    = 1e-6;  // absolute tolerance
         for(i = 0; i < nx; i++)
         {     ok &= CppAD::NearEqual(
                   check_x[i],  solution.x[i],   rel_tol, abs_tol
              );
              ok &= CppAD::NearEqual(
                   check_zl[i], solution.zl[i], rel_tol, abs_tol
              );
              ok &= CppAD::NearEqual(
                   check_zu[i], solution.zu[i], rel_tol, abs_tol
              );
         }

         return ok;
    }

`

Input File: example/ipopt_solve/get_started.cpp