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

CGAL 4.8 - Linear and Quadratic Programming Solver

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QP_solver/first_nonnegative_qp_from_iterators.cpp
// example: construct a nonnegative quadratic program from given iterators
// the QP below is the first nonnegative 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::Nonnegative_quadratic_program_from_iterators
<int**, // for A
int*, // for b
CGAL::Const_oneset_iterator<CGAL::Comparison_result>, // for r
int**, // for D
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 "<="
int D1[] = {2}; // 2D_{1,1}
int D2[] = {0, 8}; // 2D_{2,1}, 2D_{2,2}
int* D[] = {D1, D2}; // D-entries on/below diagonal
int c[] = {0, -32};
int c0 = 64; // constant term
// now construct the quadratic program; the first two parameters are
// the number of variables and the number of constraints (rows of A)
Program qp (2, 2, A, b, r, D, c, c0);
// solve the program, using ET as the exact type
Solution s = CGAL::solve_nonnegative_quadratic_program(qp, ET());
// output solution
std::cout << s;
return 0;
}