The GNU Linear Programming Kit (GLPK) is a software package intended for solving large-scale

linear programming Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear function#As a polynomial function, li ...

(LP),

mixed integer programming Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is ...

(MIP), and other related problems. It is a set of routines written in

ANSI C ANSI C, ISO C, and Standard C are successive standards for the C programming language published by the American National Standards Institute (ANSI) and ISO/IEC JTC 1/SC 22/WG 14 of the International Organization for Standardization (ISO) and the ...

and organized in the form of a callable

library A library is a collection of materials, books or media that are accessible for use and not just for display purposes. A library provides physical (hard copies) or digital access (soft copies) materials, and may be a physical location or a vir ...

. The package is part of the

GNU Project The GNU Project () is a free software, mass collaboration project announced by Richard Stallman on September 27, 1983. Its goal is to give computer users freedom and control in their use of their computers and computing devices by collaborati ...

and is released under the

GNU General Public License The GNU General Public License (GNU GPL or simply GPL) is a series of widely used free software licenses that guarantee end users the Four Freedoms (Free software), four freedoms to run, study, share, and modify the software. The license was th ...

. Problems can be modeled in the language GNU MathProg (previously known as GMPL) which shares many parts of the syntax with

AMPL AMPL (A Mathematical Programming Language) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (i.e., large-scale optimization and scheduling-type problems). It was developed b ...

and solved with standalone solver GLPSOL. GLPK can also be used as a C

. GLPK uses the revised simplex method and the primal-dual

interior point method Interior-point methods (also referred to as barrier methods or IPMs) are a certain class of algorithms that solve linear and nonlinear convex optimization problems. An interior point method was discovered by Soviet mathematician I. I. Dikin in 1 ...

for non-integer problems and the

branch-and-bound Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate soluti ...

algorithm together with Gomory's mixed integer cuts for (mixed) integer problems. GLPK is supported in the free edition of the

OptimJ OptimJ is an extension for Java with language support for writing optimization models and abstractions for bulk data processing. The extensions and the proprietary product implementing the extensions were developed by Ateji which went out of busine ...

modeling system An independent project provides a

Java Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's List ...

-based interface to GLPK (via JNI). This allows Java applications to call out to GLPK in a relatively transparent manner.

History

GLPK was developed by Andrew O. Makhorin (Андрей Олегович Махорин) of the

Moscow Aviation Institute Moscow Aviation Institute (National Research University) (MAI; russian: Московский авиационный институт, МАИ) is one of the major engineering institutes in Moscow, Russia. Since its inception MAI has been spearhe ...

. The first public release was in October 2000. * Version 1.1.1 contained a library for a revised primal and dual simplex algorithm. * Version 2.0 introduced an implementation of the primal-dual interior point method. * Version 2.2 added branch and bound solving of mixed integer problems. * Version 2.4 added a first implementation of the GLPK/L modeling language. * Version 4.0 replaced GLPK/L by the GNU MathProg modeling language, which is a subset of the

modeling language.

References

External links

GLPK official site
* GLPK Wikibook {{Mathematical optimization software Linear Programming Kit Mathematical optimization software Free mathematics software Free software programmed in C Mathematics software for Linux

History

References

Further reading

External links