/* $Id: get_started.cpp 2689 2012-12-30 20:23:29Z bradbell $ */
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-12 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the 
                    Eclipse Public License Version 1.0.

A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */

/*

$begin ipopt_solve_get_started.cpp$$
$spell
	cppad_nlp
	IpoptDir
	CppAD
$$
$index example, nonlinear, programming$$
$index programming, nonlinear example$$
$index ipopt, AD example$$

$section Nonlinear Programming Using CppAD and Ipopt: Example and Test$$

$head Purpose$$
This example program demonstrates how to use $cref ipopt_solve$$ to
solve the example problem in the Ipopt documentation; i.e., the problem
$latex \[
\begin{array}{lc}
{\rm minimize \; }      &  x_1 * x_4 * (x_1 + x_2 + x_3) + x_3
\\
{\rm subject \; to \; } &  x_1 * x_2 * x_3 * x_4  \geq 25
\\
                        &  x_1^2 + x_2^2 + x_3^2 + x_4^2 = 40
\\
                        &  1 \leq x_1, x_2, x_3, x_4 \leq 5  
\end{array}
\] $$


$head Configuration Requirement$$
This example will be compiled and tested provided that
$cref ipopt_prefix$$ is specified on the $cref cmake$$ command line.

$code
$verbatim%example/ipopt_solve/get_started.cpp%0%// BEGIN C++%// END C++%1%$$
$$

$end
*/
// BEGIN C++
# 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"; 
	// 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;
}
// END C++
