abs_normal lp_box: Example and Test

lp_box.cpp

@(@\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}} }@)@ This is cppad-20221105 documentation. Here is a link to its current documentation . abs_normal lp_box: Example and Test
Problem
Our original problem is @[@ \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} @]@

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;
}

Input File: example/abs_normal/lp_box.cpp