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

CGAL 4.8 - Linear and Quadratic Programming Solver

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QP_solver/first_lp_from_iterators.cpp
// example: construct a linear program from given iterators
// the LP below is the first linear 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::Linear_program_from_iterators
<int**, // for A
int*, // for b
CGAL::Const_oneset_iterator<CGAL::Comparison_result>, // for r
bool*, // for fl
int*, // for l
bool*, // for fu
int*, // for u
int*> // for c
Program;
typedef CGAL::Quadratic_program_solution<ET> Solution;
int main() {
int Ax[] = {1, -1}; // column for x
int Ay[] = {1, 2}; // column for y
int* A[] = {Ax, Ay}; // A comes columnwise
int b[] = {7, 4}; // right-hand side
CGAL::Const_oneset_iterator<CGAL::Comparison_result>
r( CGAL::SMALLER); // constraints are "<="
bool fl[] = {true, true}; // both x, y are lower-bounded
int l[] = {0, 0};
bool fu[] = {false, true}; // only y is upper-bounded
int u[] = {0, 4}; // x's u-entry is ignored
int c[] = {0, -32};
int c0 = 64; // constant term
// now construct the linear program; the first two parameters are
// the number of variables and the number of constraints (rows of A)
Program lp (2, 2, A, b, r, fl, l, fu, u, c, c0);
// solve the program, using ET as the exact type
Solution s = CGAL::solve_linear_program(lp, ET());
// output solution
std::cout << s;
return 0;
}