\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.12 - Linear and Quadratic Programming Solver
Linear and Quadratic Programming Solver Reference

Kaspar Fischer, Bernd Gärtner, Sven Schönherr, and Frans Wessendorp
This package contains algorithms for minimizing linear and convex quadratic functions over polyhedral domains, described by linear equations and inequalities. The algorithms are exact, i.e. the solution is computed in terms of multiprecision rational numbers. The resulting solution is certified: along with the claims that the problem under consideration has an optimal solution, is infeasible, or is unbounded, the algorithms also deliver proofs for these facts. These proofs can easily (and independently from the algorithms) be checked for correctness. The solution algorithms are based on a generalization of the simplex method to quadratic objective functions.

Introduced in: CGAL 3.3
BibTeX: cgal:fgsw-lqps-18a
License: GPL

Classified Reference Pages



There is a class that represents the solution of a linear or quadratic program. An instance of this class is returned by any of the solution functions below.

We offer a number of predefined models for the above program concepts. The following two are simultaneously models for all four concepts and are probably the most convenient models; they allow you to construct linear or quadratic programs entry by entry, or from streams in MPSFormat. At any time, you can query these programs for linearity and nonnegativity and thus select the appropriate solution function.

Then there are specific models for any of the four program concepts above; these are useful if you want to maintain the program data yourself, since they simply wrap random access iterators over the program data and involve no further copying of data.


In case you want to construct a program from complicated iterators (whose types you don't know, or simply don't want to bother with), we provide four makers.

There are four functions to solve a program, one for each program concept:

The solution process can customized by passing an object of the class

Programs can be written to an output stream in MPSFormat, using one of the following four functions:


 This module provides high and low level classes that allow to construct and represent linear and quadratic programs and their solution.
 This module provides makers to construct a program, as well as functions to solve and print programs.