/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the
                    GNU General Public License Version 3.

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 qp_interior.cpp$$
$spell
	qp
$$

$section abs_normal qp_interior: Example and Test$$

$head Problem$$
Our original problem is
$latex \[
	\R{minimize} \; | u - 1| \; \R{w.r.t} \; u \in \B{R}
\] $$
We reformulate this as the following problem
$latex \[
\begin{array}{rlr}
	\R{minimize}      & v             & \R{w.r.t} \; (u,v) \in \B{R}^2 \\
	\R{subject \; to} &  u - 1 \leq v \\
	                  &  1 - u \leq v
\end{array}
\] $$
This is equivalent to
$latex \[
\begin{array}{rlr}
	\R{minimize}
	& (0, 1) \cdot (u, v)^T  & \R{w.r.t} \; (u,v) \in \B{R}^2 \\
	\R{subject \; to}
	&
	\left( \begin{array}{cc} 1 & -1 \\ -1 & -1 \end{array} \right)
	\left( \begin{array}{c} u \\ v \end{array} \right)
	+
	\left( \begin{array}{c} -1 \\ 1 \end{array} \right)
	\leq
	0
\end{array}
\] $$
which is in the form expected by $cref qp_interior$$.


$head Source$$
$srcfile%example/abs_normal/qp_interior.cpp%
	0%// BEGIN C++%// END C++%
1%$$

$end
*/
// BEGIN C++
# include <limits>
# include <cppad/utility/vector.hpp>
# include "qp_interior.hpp"

bool qp_interior(void)
{	bool ok = true;
	typedef CppAD::vector<double> vector;
	//
	size_t n = 2;
	size_t m = 2;
	vector C(m*n), c(m), G(n*n), g(n), xin(n), xout(n), yout(m), sout(m);
	C[ 0 * n + 0 ] =  1.0; // C(0,0)
	C[ 0 * n + 1 ] = -1.0; // C(0,1)
	C[ 1 * n + 0 ] = -1.0; // C(1,0)
	C[ 1 * n + 1 ] = -1.0; // C(1,1)
	//
	c[0]           = -1.0;
	c[1]           =  1.0;
	//
	g[0]           =  0.0;
	g[1]           =  1.0;
	//
	// G = 0
	for(size_t i = 0; i < n * n; i++)
		G[i] = 0.0;
	//
	// If (u, v) = (0,2), C * (u, v) + c = (-2,-2)^T + (1,-1)^T < 0
	// Hence (0, 2) is feasible.
	xin[0] = 0.0;
	xin[1] = 2.0;
	//
	double epsilon = 99.0 * std::numeric_limits<double>::epsilon();
	size_t maxitr  = 10;
	size_t level   = 0;
	//
	ok &= CppAD::qp_interior(
		level, c, C, g, G, epsilon, maxitr, xin, xout, yout, sout
	);
	//
	// check optimal value for u
	ok &= std::fabs( xout[0] - 1.0 ) < epsilon;
	// check optimal value for v
	ok &= std::fabs( xout[1] ) < epsilon;
	//
	return ok;
}
// END C++
