\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

lp_box.cpp

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abs_normal lp_box: Example and Test

Problem

Our original problem is

\[\begin{split}\begin{array}{rl} \R{minimize} & x_0 - x_1 \; \R{w.r.t} \; x \in \B{R}^2 \\ \R{subject \; to} & -2 \leq x_0 \leq +2 \; \R{and} \; -2 \leq x_1 \leq +2 \end{array}\end{split}\]

Source

# include <limits>
# include <cppad/utility/vector.hpp>
# include "lp_box.hpp"

bool lp_box(void)
{  bool ok = true;
   typedef CppAD::vector<double> vector;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   size_t n = 2;
   size_t m = 0;
   vector A(m), b(m), c(n), d(n), xout(n);
   c[0] = +1.0;
   c[1] = -1.0;
   //
   d[0] = +2.0;
   d[1] = +2.0;
   //
   size_t level   = 0;
   size_t maxitr  = 20;
   //
   ok &= CppAD::lp_box(level, A, b, c, d, maxitr, xout);
   //
   // check optimal value for x
   ok &= std::fabs( xout[0] + 2.0 ) < eps99;
   ok &= std::fabs( xout[1] - 2.0 ) < eps99;
   //
   return ok;
}