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// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-24 Bradley M. Bell
// ----------------------------------------------------------------------------
/*
{xrst_begin ipopt_nlp_get_started.cpp dev}
{xrst_spell
lc
}
Nonlinear Programming Using CppAD and Ipopt: Getting Started
############################################################
Purpose
*******
This example program demonstrates how to use the class cppad_ipopt_nlp to
solve the example problem in the Ipopt documentation; i.e., the problem
.. math::
\begin{array}{lc}
{\rm minimize \; } & x_1 * x_4 * (x_1 + x_2 + x_3) + x_3
\\
{\rm subject \; to \; } & x_1 * x_2 * x_3 * x_4 \geq 25
\\
& x_1^2 + x_2^2 + x_3^2 + x_4^2 = 40
\\
& 1 \leq x_1, x_2, x_3, x_4 \leq 5
\end{array}
Configuration Requirement
*************************
This example will be compiled and tested provided that
a ``include_ipopt=true``
is specified on the :ref:`cmake-name` command line.
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end ipopt_nlp_get_started.cpp}
*/
// BEGIN C++
# include <cppad_ipopt_nlp.hpp>
namespace {
using namespace cppad_ipopt;
class FG_info : public cppad_ipopt_fg_info
{
private:
bool retape_;
public:
// derived class part of constructor
FG_info(bool retape_in)
: retape_ (retape_in)
{ }
// Evaluation of the objective f(x), and constraints g(x)
// using an Algorithmic Differentiation (AD) class.
ADVector eval_r(size_t k, const ADVector& x)
{ ADVector fg(3);
// Fortran style indexing
ADNumber x1 = x[0];
ADNumber x2 = x[1];
ADNumber x3 = x[2];
ADNumber 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 fg;
}
bool retape(size_t k)
{ return retape_; }
};
}
bool ipopt_get_started(void)
{ bool ok = true;
size_t j;
// number of independent variables (domain dimension for f and g)
size_t n = 4;
// number of constraints (range dimension for g)
size_t m = 2;
// initial value of the independent variables
NumberVector x_i(n);
x_i[0] = 1.0;
x_i[1] = 5.0;
x_i[2] = 5.0;
x_i[3] = 1.0;
// lower and upper limits for x
NumberVector x_l(n);
NumberVector x_u(n);
for(j = 0; j < n; j++)
{ x_l[j] = 1.0;
x_u[j] = 5.0;
}
// lower and upper limits for g
NumberVector g_l(m);
NumberVector g_u(m);
g_l[0] = 25.0; g_u[0] = 1.0e19;
g_l[1] = 40.0; g_u[1] = 40.0;
size_t icase;
for(icase = 0; icase <= 1; icase++)
{ // Should cppad_ipopt_nlp retape the operation sequence for
// every new x. Can test both true and false cases because
// the operation sequence does not depend on x (for this case).
bool retape = icase != 0;
// object in derived class
FG_info fg_info(retape);
// create the Ipopt interface
cppad_ipopt_solution solution;
Ipopt::SmartPtr<Ipopt::TNLP> cppad_nlp = new cppad_ipopt_nlp(
n, m, x_i, x_l, x_u, g_l, g_u, &fg_info, &solution
);
// Create an instance of the IpoptApplication
using Ipopt::IpoptApplication;
Ipopt::SmartPtr<IpoptApplication> app = new IpoptApplication();
// turn off any printing
app->Options()->SetIntegerValue("print_level", 0);
app->Options()->SetStringValue("sb", "yes");
// maximum number of iterations
app->Options()->SetIntegerValue("max_iter", 10);
// approximate accuracy in first order necessary conditions;
// see Mathematical Programming, Volume 106, Number 1,
// Pages 25-57, Equation (6)
app->Options()->SetNumericValue("tol", 1e-9);
// derivative testing
app->Options()->
SetStringValue("derivative_test", "second-order");
app->Options()-> SetNumericValue(
"point_perturbation_radius", 0.
);
// Initialize the IpoptApplication and process the options
Ipopt::ApplicationReturnStatus status = app->Initialize();
ok &= status == Ipopt::Solve_Succeeded;
// Run the IpoptApplication
status = app->OptimizeTNLP(cppad_nlp);
ok &= status == Ipopt::Solve_Succeeded;
/*
Check some of the solution values
*/
ok &= solution.status == cppad_ipopt_solution::success;
//
double check_x[] = { 1.000000, 4.743000, 3.82115, 1.379408 };
double check_z_l[] = { 1.087871, 0., 0., 0. };
double check_z_u[] = { 0., 0., 0., 0. };
double rel_tol = 1e-6; // relative tolerance
double abs_tol = 1e-6; // absolute tolerance
for(j = 0; j < n; j++)
{ ok &= CppAD::NearEqual(
check_x[j], solution.x[j], rel_tol, abs_tol
);
ok &= CppAD::NearEqual(
check_z_l[j], solution.z_l[j], rel_tol, abs_tol
);
ok &= CppAD::NearEqual(
check_z_u[j], solution.z_u[j], rel_tol, abs_tol
);
}
}
return ok;
}
// END C++
|
