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

CGAL 4.8 - Linear and Quadratic Programming Solver

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QP_solver/convex_hull_containment_benchmarks.cpp
// Example: assess the solver performance under any of the available
// pricing strategies, in the convex-hull-containment problem
// NOTE: in order to see meaningful results, compile with -DNDEBUG
#include <vector>
#include <CGAL/Cartesian_d.h>
#include <CGAL/MP_Float.h>
#include <CGAL/Random.h>
#include <CGAL/Timer.h>
#include "solve_convex_hull_containment_lp3.h"
// choose exact floating-point type
#ifdef CGAL_USE_GMP
#include <CGAL/Gmpzf.h>
typedef CGAL::Gmpzf ET;
#else
#include <CGAL/MP_Float.h>
typedef CGAL::MP_Float ET;
#endif
typedef CGAL::Cartesian_d<double> Kernel_d;
typedef Kernel_d::Point_d Point_d;
int main()
{
const int d = 10; // change this in order to experiment
const int n = 100000; // change this in order to experiment
// generate n random d-dimensional points in [0,1]^d
CGAL::Random rd;
std::vector<Point_d> points;
for (int j =0; j<n; ++j) {
std::vector<double> coords;
for (int i=0; i<d; ++i)
coords.push_back(rd.get_double());
points.push_back (Point_d (d, coords.begin(), coords.end()));
}
// benchmark all pricing strategies in turn
CGAL::Quadratic_program_pricing_strategy strategy[] = {
CGAL::QP_CHOOSE_DEFAULT, // QP_PARTIAL_FILTERED_DANTZIG
CGAL::QP_DANTZIG, // Dantzig's pivot rule...
CGAL::QP_PARTIAL_DANTZIG, // ... with partial pricing
CGAL::QP_BLAND, // Bland's pivot rule
CGAL::QP_FILTERED_DANTZIG, // Dantzig's filtered pivot rule...
CGAL::QP_PARTIAL_FILTERED_DANTZIG // ... with partial pricing
};
CGAL::Timer t;
for (int i=0; i<6; ++i) {
// test strategy i
CGAL::Quadratic_program_options options;
options.set_pricing_strategy (strategy[i]);
t.reset(); t.start();
// is origin in convex hull of the points? (most likely, not)
solve_convex_hull_containment_lp
(Point_d (d, CGAL::ORIGIN), points.begin(), points.end(),
ET(0), options);
t.stop();
std::cout << "Time (s) = " << t.time() << std::endl;
}
return 0;
}