GNU Linear Programming Kit

GNU Linear Programming KitOriginal author(s)| Andrew O. Makhorin

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Developer(s)| GNU Project
Written in| C
Operating system| Cross-platform
Available in| English
License| GPLv3
Website| www.gnu.org/software/glpk/

The GNU Linear Programming Kit (GLPK) is a software package intended for solving large-scale linear programming (LP), mixed integer programming (MIP), and other related problems. It is a set of routines written in ANSI C and organized in the form of a callable library. The package is part of the GNU Project and is released under the GNU General Public License.

GLPK uses the revised simplex method and the primal-dual interior point method for non-integer problems and the branch-and-bound algorithm together with Gomory's mixed integer cuts for (mixed) integer problems.

## Contents

* 1 History
* 2 Interfaces and wrappers
* 3 Further reading
* 4 References
* 5 External links

## History

GLPK was developed by Andrew O. Makhorin (Андрей Олегович Махорин) of the Moscow Aviation Institute. 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 AMPL modeling language.

## Interfaces and wrappers

Since version 4.0, GLPK problems can be modeled using GNU MathProg (GMPL), a subset of the AMPL modeling language used only by GLPK. However, GLPK is most commonly called from other programming languages. Wrappers exist for:

* Julia[1] and the JuMP modeling package[2]
* Java (using OptimJ)[3]

## Further reading

| Wikibooks has a book on the topic of: GLPK

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* Eiji Oki (2012). Linear Programming and Algorithms for Communication Networks: A Practical Guide to Network Design, Control, and Management. CRC Press. ISBN 978-1-4665-5264-7. The book uses GLPK exclusively and contains numerous examples.

## References

1. ↑ GLPK.jl, JuMP-dev, 2023-01-16, https://github.com/jump-dev/GLPK.jl, retrieved 2023-02-04
2. ↑ jump-dev/JuMP.jl, JuMP-dev, 2023-02-04, https://github.com/jump-dev/JuMP.jl, retrieved 2023-02-04
3. ↑ "GLPK for Java – About". http://glpk-java.sourceforge.net.

## External links

* GLPK official site
* GLPK Wikibook

* v
* t
* e

Mathematical optimization software

Data formats|

* Mathematica
* MPS
* nl
* sol

Modeling tools|

* AIMMS
* AMPL
* APMonitor
* ECLiPSe-CLP
* GEKKO
* GAMS
* GNU MathProg
* JuMP
* LINDO
* OPL
* Mathematica
* OptimJ
* PuLP
* Pyomo
* TOMLAB
* Xpress-Mosel
* ZIMPL

LP, MILP∗ solvers|

* APOPT∗
* Artelys Knitro∗
* BCP∗
* CLP
* CBC∗
* CPLEX∗
* FortMP∗
* GCG∗
* GLPK/GLPSOL∗
* Gurobi∗
* LINDO∗
* Lp_solve
* LOQO
* Mathematica
* MINOS
* MINTO∗
* MOSEK∗
* SCIP∗
* SoPlex
* SYMPHONY∗
* Xpress-Optimizer∗

QP, MIQP∗ solvers|

* APOPT∗
* Artelys Knitro∗
* CBC∗
* CLP
* CPLEX∗
* FortMP∗
* Gurobi∗
* IPOPT
* LINDO∗
* Mathematica
* MINOS
* MOSEK∗
* SCIP∗
* Xpress-Optimizer∗

QCP, MIQCP∗ solvers|

* APOPT∗
* Artelys Knitro∗
* CPLEX∗
* Gurobi∗
* IPOPT
* LINDO∗
* Mathematica
* MINOS
* MOSEK∗
* SCIP∗
* Xpress-Optimizer∗
* Xpress-SLP∗

SOCP, MISOCP∗ solvers|

* Artelys Knitro∗
* CPLEX∗
* Gurobi∗
* LINDO∗
* LOQO
* Mathematica
* MOSEK∗
* SCIP∗
* Xpress-Optimizer∗

SDP, MISDP∗ solvers|

* Mathematica
* MOSEK

NLP, MINLP∗ solvers|

* AOA∗
* APOPT∗
* Artelys Knitro∗
* BARON∗
* Couenne∗
* Galahad library
* IPOPT
* LINDO∗
* LOQO
* MIDACO∗
* MINOS
* NLPQLP
* NPSOL
* SCIP∗
* SNOPT∗
* WORHP
* Xpress-SLP∗

GO solvers|

* BARON
* Couenne∗
* Mathematica
* LINDO
* SCIP

CP solvers|

* Comet
* CPLEX CP Optimizer
* Gecode
* Mathematica
* JaCoP

Metaheuristic solvers|

* OptaPlanner

* List of optimization software
* Comparison of optimization software

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