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

CGAL 4.8 - Linear and Quadratic Programming Solver

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QP_solver/first_nonnegative_lp.cpp
// example: construct a nonnegative linear program from data
// the LP below is the first nonnegative linear program example
// in the user manual
#include <iostream>
#include <cassert>
#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 LP with Ax <= b
Program lp (CGAL::SMALLER, true, 0, false, 0);
// now set the non-default entries
const int X = 0;
const int Y = 1;
lp.set_a(X, 0, 1); lp.set_a(Y, 0, 1); lp.set_b(0, 7); // x + y <= 7
lp.set_a(X, 1, -1); lp.set_a(Y, 1, 2); lp.set_b(1, 4); // -x + 2y <= 4
lp.set_c(Y, -32); // -32y
// solve the program, using ET as the exact type
Solution s = CGAL::solve_nonnegative_linear_program(lp, ET());
assert (s.solves_nonnegative_linear_program(lp));
// output solution
std::cout << s;
return 0;
}