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

qp_box.cpp

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abs_normal qp_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 "qp_box.hpp"

bool qp_box(void)
{   bool ok = true;
    typedef CppAD::vector<double> vector;
    //
    size_t n = 2;
    size_t m = 0;
    vector a(n), b(n), c(m), C(m), g(n), G(n*n), xin(n), xout(n);
    a[0] = -2.0;
    a[1] = -2.0;
    b[0] = +2.0;
    b[1] = +2.0;
    g[0] = +1.0;
    g[1] = -1.0;
    for(size_t i = 0; i < n * n; i++)
        G[i] = 0.0;
    //
    // (0, 0) is feasible.
    xin[0] = 0.0;
    xin[1] = 0.0;
    //
    size_t level   = 0;
    double epsilon = 99.0 * std::numeric_limits<double>::epsilon();
    size_t maxitr  = 20;
    //
    ok &= CppAD::qp_box(
        level, a, b, c, C, g, G, epsilon, maxitr, xin, xout
    );
    //
    // check optimal value for x
    ok &= std::fabs( xout[0] + 2.0 ) < epsilon;
    ok &= std::fabs( xout[1] - 2.0 ) < epsilon;
    //
    return ok;
}