Comparison of optimization software

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 the 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 while the output can be the power consumption. Other inputs can be business choices with the output being obtained profit. or describing the configuration of a physical system with the output being its energy.

An optimization problem can be represented in the following way

Given: a function f : A ${\displaystyle \to }$ 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 notable optimization software libraries, either specialized or general purpose libraries with significant optimization coverage.

Name	Programming language	Latest stable version	Academic/noncommercial use is free	Can be used in proprietary apps	License	Notes
ALGLIB	C++, C#, Python, FreePascal	3.19.0 / June 2022	Yes	Yes	Dual (Commercial, GPL)	General purpose library, includes optimization package: linear, quadratic, nonlinear programming.
AMPL	C, C++, C#, Python, Java, Matlab, R	October 2018	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.
APMonitor	Fortran, C++, Python, Matlab, Julia	0.6.2 / March 2016	Yes	Yes	Dual (Commercial, academic)	A differential and algebraic modeling language for mixed-integer and nonlinear optimization. Freely available interfaces for Matlab, Python, and Julia.
Artelys Knitro	C, C++, C#, Python, Java, Julia, Matlab, R	11.1 / November 2018	No	Yes	Commercial, Academic, Trial	General purpose library, specialized in nonlinear optimization. Handles mixed-integer problems (MINLP) and mathematical programs with equilibrium constraints (MPEC). Specialized algorithms for nonlinear least squares problems.
CPLEX	C, C++, Java, C#, Python, R	20.1 / Dec 2020	Yes	Yes	Commercial, academic, trial	IBM CPLEX Optimization Studio is a suite of optimization engines (CPLEX for Mathematical Programming, and CP Optimizer for Constraint programming), a modeling language (OPL), and an Integrated Development Environment.
FICO Xpress	Mosel, BCL, C, C++, Java, R, Python, Matlab, .Net, VB6	8.13 / Nov 2021	Yes	Yes	Commercial, academic, community, trial	Suite of Optimization Technologies and Solutions. Includes: Solver technologies including (LP (Simplex & Barrier), MIP, MIQP, MIQCQP, MISOCP, MINLP QP, QCQP, SOCP, NLP (SLP & Interior Point); An algebraic modelling and procedural programming language; an Integrated Development Environment; Supports for a range of execution services; Support for packaging of optimization models and services as software solutions
GEKKO	Python	0.2.8 / August 2020	Yes	Yes	Dual (Commercial, academic)	GEKKO is a Python package for machine learning and optimization of mixed-integer and differential algebraic equations. It is coupled with large-scale solvers for linear, quadratic, nonlinear, and mixed integer programming (LP, QP, NLP, MILP, MINLP). Modes of operation include parameter regression, data reconciliation, real-time optimization, dynamic simulation, and nonlinear predictive control.
GNU Linear Programming Kit	C	4.52 / July 2013	Yes	No	GPL	Free library for linear programming (LP) and mixed integer programming (MIP).
GNU Scientific Library	C	1.16 / July 2013	Yes	No	GPL	Free library provided by GNU project.
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]
Math Kernel Library (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.
Wolfram Mathematica	C++, Wolfram Language	14.2.0 (January 23, 2025; 4 months ago (2025-01-23)) [±][3]	No	Yes	Proprietary	Constrained nonlinear optimization, interior point methods, convex optimization and integer programming-as well as original symbolic methods integrated with general computational capabilities.
MIDACO	C++, C#, Python, Matlab, Octave, Fortran, R, Java, Excel, VBA, Julia	6.0 / Mar 2018	Yes	Yes	Dual (Commercial, academic)	Lightweight software tool for single- and multi-objective optimization. Supporting MINLP and parallelization.
NAG Numerical Libraries	C, Fortran	Mark 26 / October 2017	No	Yes	Proprietary
NMath	C#	5.3 / May 2013	No	Yes	Proprietary	C# numerical library built on top of MKL.
Octeract Engine	C++/Python	0.11.29 / November 2019	No	Yes	Commercial	Supercomputing deterministic global optimization solver for general MINLP problems. Octeract Engine uses MPI for distributed calculations.
OptaPlanner	Java	8.0.0.Final / November 2020	Yes	Yes	ASL (open source)	Lightweight optimization solver in Java, with optional integration modules for JPA-Hibernate, Quarkus, Spring, Jackson, JAXB, etc. Works on Kotlin and Scala too.
SciPy	Python	0.13.1 / November 2013	Yes	Yes	BSD	General purpose numerical and scientific computing library for Python.

See also

• List of optimization software