\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Linear and Quadratic Programming Solver

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QP_solver/first_qp_basic_constraints.cpp
// example: output basic constraint indices
// the QP below is the first quadratic program example in the user manual
#include <iostream>
#include <CGAL/basic.h>
#include <CGAL/QP_models.h>
#include <CGAL/QP_functions.h>
// choose exact integral type
#ifdef CGAL_USE_GMP
#include <CGAL/Gmpz.h>
typedef CGAL::Gmpz ET;
#else
#include <CGAL/MP_Float.h>
typedef CGAL::MP_Float ET;
#endif
// program and solution types
typedef CGAL::Quadratic_program<int> Program;
typedef CGAL::Quadratic_program_solution<ET> Solution;
int main() {
// by default, we have a nonnegative QP with Ax <= b
Program qp (CGAL::SMALLER, true, 0, false, 0);
// now set the non-default entries: 0 <-> x, 1 <-> y
qp.set_a(0, 0, 1); qp.set_a(1, 0, 1); qp.set_b(0, 7); // x + y <= 7
qp.set_a(0, 1, -1); qp.set_a(1, 1, 2); qp.set_b(1, 4); // -x + 2y <= 4
qp.set_u(1, true, 4); // y <= 4
qp.set_d(0, 0, 2); qp.set_d (1, 1, 8); // x^2 + 4 y^2
qp.set_c(1, -32); // -32y
qp.set_c0(64); // +64
// solve the program, using ET as the exact type
Solution s = CGAL::solve_quadratic_program(qp, ET());
// print basic constraint indices (we know that there is only one: 1)
if (s.is_optimal()) { // we know that, don't we?
std::cout << "Basic constraints: ";
for (Solution::Index_iterator it = s.basic_constraint_indices_begin();
it != s.basic_constraint_indices_end(); ++it)
std::cout << *it << " ";
std::cout << std::endl;
}
return 0;
}