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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 qp_interior.cpp}
{xrst_spell
rlr
}
abs_normal qp_interior: Example and Test
########################################
Problem
*******
Our original problem is
.. math::
\R{minimize} \; | u - 1| \; \R{w.r.t} \; u \in \B{R}
We reformulate this as the following problem
.. math::
\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
.. math::
\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 :ref:`qp_interior-name` .
Source
******
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end qp_interior.cpp}
*/
// 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++
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