# Comparison of optimization software

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Given a system transforming a set of inputs to output values, described by a mathematical function f, optimization refers to the generation and selection of a best solution from some set of available alternatives,[1] by systematically choosing input values from within an allowed set, computing the value of the function, and recording the best value found during the process. Many real-world and theoretical problems may be modeled in this general framework. For example, the inputs can be design parameters of a motor, the output can be the power consumption, or the inputs can be business choices and the output can be the obtained profit, or the inputs can describe the configuration of a physical system and the output can be its energy.

An optimization problem can be represented in the following way

Given: a function f : A $\to$ R from some set A to the real numbers
Search for: an element x0 in A such that f(x0) ≤ f(x) for all x in A ("minimization").

Typically, A is some subset of the Euclidean space Rn, often specified by a set of constraints, equalities or inequalities that the members of A have to satisfy. Maximization can be reduced to minimization by multiplying the function by minus one.

The use of optimization software requires that the function f is defined in a suitable programming language and linked to the optimization software. The optimization software will deliver input values in A, the software module realizing f will deliver the computed value f(x). In this manner, a clear separation of concerns is obtained: different optimization software modules can be easily tested on the same function f, or a given optimization software can be used for different functions f.

The following tables provide a comparison of optimization software libraries, either specialized or general purpose libraries with significant optimization coverage.

Language Latest stable version Academic/noncommercial
use is free
Can be used in
proprietary aps
License Notes
ALGLIB C++, C#, FreePascal, VBA 3.8.0 / August 2013 Yes Yes Dual (Commercial, GPL) General purpose library, includes optimization package.
AMPL C October 2013 Yes Yes Dual (Commercial, academic) A popular algebraic modeling language for linear, mixed-integer and nonlinear optimization. Student and AMPL for courses versions are available for free.
GNU Scientific Library C 1.16 / July 2013 Yes No GPL Free library provided by GNU project.
GNU Linear Programming Kit C 4.52 / July 2013 Yes No GPL Free library for linear programming (LP) and mixed integer programming (MIP).
IMSL Numerical Libraries C, Java, C#, Fortran, Python many components No Yes Proprietary
LIONsolver C++, Java 2.0.198 / October 2011 Yes Yes Proprietary Support for interactive and learning optimization,

according to RSO principles .[2]

MKL C++, Fortran 11.1 / October 2013 No Yes Proprietary Numerical library from Intel. MKL is specialized on linear algebra,
but contains some optimization-related functionality.
NAG Numerical Libraries C, Fortran Mark 24 / October 2013 No Yes Proprietary
NMath C# 5.3 / May 2013 No Yes Proprietary C# numerical library built on top of MKL.
OptaPlanner Java 6.0.1.Final / Dec 2013 Yes Yes ASL Lightweight optimization solver in Java
SciPy Python 0.13.1 / November 2013 Yes Yes BSD General purpose numerical library from Enthought.

## References

1. ^ "The Nature of Mathematical Programming," Mathematical Programming Glossary, INFORMS Computing Society.
2. ^ Battiti, Roberto; Mauro Brunato; Franco Mascia (2008). Reactive Search and Intelligent Optimization. Springer Verlag. ISBN 978-0-387-09623-0.