<?xml version='1.0'?>
<?xml-stylesheet type='text/xsl' href='pmathml.xsl'?>
<html xmlns='http://www.w3.org/1999/xhtml'>
<head>
<title>Nonlinear Programming Using CppAD and Ipopt: Example and Test</title>
<meta name="description" id="description" content="Nonlinear Programming Using CppAD and Ipopt: Example and Test"/>
<meta name="keywords" id="keywords" content=" example nonlinear programming ipopt Ad "/>
<style type='text/css'>
body { color : black }
body { background-color : white }
A:link { color : blue }
A:visited { color : purple }
A:active { color : purple }
</style>
<script type='text/javascript' language='JavaScript' src='_ipopt_get_started.cpp_xml.js'>
</script>
</head>
<body>
<table><tr>
<td>
<a href="http://www.coin-or.org/CppAD/" target="_top"><img border="0" src="_image.gif"/></a>
</td>
<td><a href="ipopt_cppad_windows.xml" target="_top">Prev</a>
</td><td><a href="ipopt_cppad_ode.xml" target="_top">Next</a>
</td><td>
<select onchange='choose_across0(this)'>
<option>Index-></option>
<option>contents</option>
<option>reference</option>
<option>index</option>
<option>search</option>
<option>external</option>
</select>
</td>
<td>
<select onchange='choose_up0(this)'>
<option>Up-></option>
<option>CppAD</option>
<option>Example</option>
<option>General</option>
<option>ipopt_cppad_nlp</option>
<option>ipopt_get_started.cpp</option>
</select>
</td>
<td>
<select onchange='choose_down3(this)'>
<option>Example-></option>
<option>General</option>
<option>ExampleUtility</option>
<option>ListAllExamples</option>
<option>test_vector</option>
</select>
</td>
<td>
<select onchange='choose_down2(this)'>
<option>General-></option>
<option>ad_fun.cpp</option>
<option>ad_in_c.cpp</option>
<option>HesMinorDet.cpp</option>
<option>HesLuDet.cpp</option>
<option>ipopt_cppad_nlp</option>
<option>Interface2C.cpp</option>
<option>JacMinorDet.cpp</option>
<option>JacLuDet.cpp</option>
<option>mul_level</option>
<option>OdeStiff.cpp</option>
<option>ode_taylor.cpp</option>
<option>ode_taylor_adolc.cpp</option>
<option>StackMachine.cpp</option>
</select>
</td>
<td>
<select onchange='choose_down1(this)'>
<option>ipopt_cppad_nlp-></option>
<option>ipopt_cppad_windows</option>
<option>ipopt_get_started.cpp</option>
<option>ipopt_cppad_ode</option>
</select>
</td>
<td>ipopt_get_started.cpp</td>
<td>
<select onchange='choose_current0(this)'>
<option>Headings-></option>
<option>Purpose</option>
<option>Configuration Requirement</option>
</select>
</td>
</tr></table><br/>
<center><b><big><big>Nonlinear Programming Using CppAD and Ipopt: Example and Test</big></big></b></center>
<br/>
<b><big><a name="Purpose" id="Purpose">Purpose</a></big></b>
<br/>
This example program demonstrates how to use the class ipopt_cppad_nlp to
solve the example problem in the Ipopt documentation; i.e., the problem
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<mtable rowalign="center" ><mtr><mtd columnalign="left" >
<mrow><mstyle mathvariant='normal'><mi mathvariant='normal'>minimize</mi>
<mspace width='.3em'/>
</mstyle></mrow>
</mtd><mtd columnalign="center" >
<msub><mi mathvariant='italic'>x</mi>
<mn>1</mn>
</msub>
<mo stretchy="false">*</mo>
<msub><mi mathvariant='italic'>x</mi>
<mn>4</mn>
</msub>
<mo stretchy="false">*</mo>
<mo stretchy="false">(</mo>
<msub><mi mathvariant='italic'>x</mi>
<mn>1</mn>
</msub>
<mo stretchy="false">+</mo>
<msub><mi mathvariant='italic'>x</mi>
<mn>2</mn>
</msub>
<mo stretchy="false">+</mo>
<msub><mi mathvariant='italic'>x</mi>
<mn>3</mn>
</msub>
<mo stretchy="false">)</mo>
<mo stretchy="false">+</mo>
<msub><mi mathvariant='italic'>x</mi>
<mn>3</mn>
</msub>
</mtd></mtr><mtr><mtd columnalign="left" >
<mrow><mstyle mathvariant='normal'><mi mathvariant='normal'>subject</mi>
<mspace width='.3em'/>
<mi mathvariant='normal'>to</mi>
<mspace width='.3em'/>
</mstyle></mrow>
</mtd><mtd columnalign="center" >
<msub><mi mathvariant='italic'>x</mi>
<mn>1</mn>
</msub>
<mo stretchy="false">*</mo>
<msub><mi mathvariant='italic'>x</mi>
<mn>2</mn>
</msub>
<mo stretchy="false">*</mo>
<msub><mi mathvariant='italic'>x</mi>
<mn>3</mn>
</msub>
<mo stretchy="false">*</mo>
<msub><mi mathvariant='italic'>x</mi>
<mn>4</mn>
</msub>
<mo stretchy="false">≥</mo>
<mn>25</mn>
</mtd></mtr><mtr><mtd columnalign="left" >
</mtd><mtd columnalign="center" >
<msubsup><mi mathvariant='italic'>x</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
<mo stretchy="false">+</mo>
<msubsup><mi mathvariant='italic'>x</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
<mo stretchy="false">+</mo>
<msubsup><mi mathvariant='italic'>x</mi>
<mn>3</mn>
<mn>2</mn>
</msubsup>
<mo stretchy="false">+</mo>
<msubsup><mi mathvariant='italic'>x</mi>
<mn>4</mn>
<mn>2</mn>
</msubsup>
<mo stretchy="false">=</mo>
<mn>40</mn>
</mtd></mtr><mtr><mtd columnalign="left" >
</mtd><mtd columnalign="center" >
<mn>1</mn>
<mo stretchy="false">≤</mo>
<msub><mi mathvariant='italic'>x</mi>
<mn>1</mn>
</msub>
<mo stretchy="false">,</mo>
<msub><mi mathvariant='italic'>x</mi>
<mn>2</mn>
</msub>
<mo stretchy="false">,</mo>
<msub><mi mathvariant='italic'>x</mi>
<mn>3</mn>
</msub>
<mo stretchy="false">,</mo>
<msub><mi mathvariant='italic'>x</mi>
<mn>4</mn>
</msub>
<mo stretchy="false">≤</mo>
<mn>5</mn>
</mtd></mtr></mtable>
</mrow></math>
<br/>
<b><big><a name="Configuration Requirement" id="Configuration Requirement">Configuration Requirement</a></big></b>
<br/>
This example will be compiled and tested provided that
the value <a href="installunix.xml#IpoptDir" target="_top"><span style='white-space: nowrap'>IpoptDir</span></a>
is specified on the
<a href="installunix.xml#Configure" target="_top"><span style='white-space: nowrap'>configure</span></a>
command line.
<code><font color="blue">
<pre style='display:inline'>
# include "ipopt_cppad_nlp.hpp"
namespace {
class FG_info : public ipopt_cppad_fg_info
{
private:
bool retape_;
public:
// derived class part of constructor
FG_info(bool retape)
: retape_ (retape)
{ }
// 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 ipopt_cppad_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
ipopt_cppad_solution solution;
Ipopt::SmartPtr<Ipopt::TNLP> cppad_nlp = new ipopt_cppad_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);
// 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");
// 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 == ipopt_cppad_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::<a href="nearequal.xml" target="_top">NearEqual</a>(
check_x[j], solution.x[j], rel_tol, abs_tol
);
ok &= CppAD::<a href="nearequal.xml" target="_top">NearEqual</a>(
check_z_l[j], solution.z_l[j], rel_tol, abs_tol
);
ok &= CppAD::<a href="nearequal.xml" target="_top">NearEqual</a>(
check_z_u[j], solution.z_u[j], rel_tol, abs_tol
);
}
}
return ok;
}
</pre>
</font></code>
<hr/>Input File: ipopt_cppad/ipopt_get_started.cpp
</body>
</html>
