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| {{unreferenced|date=August 2013}}
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| Given a transformation between input and output values, described by a [[Function (mathematics)|mathematical function]] ''f'',
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| [[Mathematical optimization|optimization]] deals with generating and selecting a best solution from some set of available alternatives, by systematically choosing input values from within an allowed set, computing the output of the function, and recording the best output values found during the process. Many real-world problems can be modeled in this way. For example,
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| the inputs can be design parameters of a motor, the output can be the power consumption, or the inputs
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| can be business choices and the output can be the obtained profit.
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| An [[optimization problem]], in this case a minimization problem, can be represented in the following way
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| :''Given:'' a [[function (mathematics)|function]] ''f'' : ''A'' <math>\to</math> '''R''' from some [[Set (mathematics)|set]] ''A'' to the [[real number]]s
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| :''Search for:'' an element ''x''<sub>0</sub> in ''A'' such that ''f''(''x''<sub>0</sub>) ≤ ''f''(''x'') for all ''x'' in ''A''.
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| In continuous optimization, ''A'' is some [[subset]] of the [[Euclidean space]] '''R'''<sup>''n''</sup>, often specified by a set of ''[[constraint (mathematics)|constraint]]s'', equalities or inequalities that the members of ''A'' have to satisfy.
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| In combinatorial optimization, ''A'' is some [[subset]] of a discrete space, like binary strings, permutations, sets of integers.
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| The use of '''optimization software''' requires that the function ''f'' is defined in a suitable
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| programming language and connected at compile or run time to
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| the optimization software. The optimization software will deliver input values in ''A'',
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| the software module realizing ''f'' will deliver the computed value ''f''(''x'') and, in some cases,
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| additional information about the function like derivatives.
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| In this manner, a clear separation of concerns is obtained: different optimization
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| software modules can be easily tested on the same function ''f'', or a given
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| optimization software can be used for different functions ''f''.
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| The following tables provide a list of optimization software organized according to license and business model type.
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| ==Free and Open Source software==
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| {| class="wikitable"
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| |-
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| !Name
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| !License
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| !Brief info
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| |-
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| |[[ADMB]] ||BSD|| nonlinear optimization framework, using [[automatic differentiation]]
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| |-
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| |[http://www.ime.usp.br/~egbirgin/tango ALGENCAN] ||[[GPL]]|| Fortran code for general nonlinear programming. Interfaces with AMPL, C/C++, CUTEr, Matlab, Python, Octave and R.
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| |-
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| |[[APMonitor]] ||BSD|| [http://apmonitor.com/wiki/index.php/Main/MATLAB MATLAB Toolbox] and [http://apmonitor.com/wiki/index.php/Main/PythonApp Python APIs] to Mixed Integer Nonlinear Programming Solvers
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| |-
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| |[[ASCEND]] ||GPL|| mathematical modelling system
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| |CONDOR ||GPL|| Non-linear Continuous Objective Function for small dimension (n<20) with linear and non-linear constraints. Only the value of the objective function is used. Stand-Alone C++ code.
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| |-
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| |[[COIN-OR SYMPHONY]] ||GPL|| integer programming
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| |[[CUTEr]] ||GPL || testing environment for optimization and linear algebra solvers
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| |[[dlib]] || [[Boost Software License | Boost ]] || A stand-alone C++ library with a variety of linear and non-linear solvers for small and large scale problems
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| |[http://www.gnu.org/software/glpk/ GLPK] ||GPL|| GNU Linear Programming Kit
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| |[[IPOPT]]||[[Common Public License|CPL]]|| large scale nonlinear optimization for continuous system (requires gradient)
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| |[http://www.joptimizer.com JOptimizer]||[[Apache License]]|| Java library for convex optimization
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| |[http://users.eecs.northwestern.edu/~nocedal/lbfgs.html L-BFGS] ||BSD|| [[L-BFGS|limited-memory quasi-Newton method]] optimization; for large scale optimization
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| |-
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| |[http://ligeropt.sourceforge.net/ Liger] ||LGPL|| Liger is an open source integrated optimization environment for single and multi-objective nonconvex problems
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| |[http://www.midaco-solver.com/ MIDACO] || BY-NC-ND || Global optimization software, Limited Version, MINLP (Matlab, Octave, Python, C/C++ and Fortran)
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| |[[MINUIT]]/MINUIT2 || (L)GPL || multivariate function minimizer for real-valued functions with analytic or numerical gradients
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| |[http://ab-initio.mit.edu/wiki/index.php/NLopt NLopt] || LGPL, [[MIT License|MIT]] || many algos, many language bindings, global and local optimizers, derivative-free and gradient-driven
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| |[http://www.gerad.ca/NOMAD NOMAD]||[[LGPL]]|| generic black-box (no gradients required) optimization package
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| |[[OpenOpt]]||[[BSD licenses|BSD]] || free numerical optimization framework in [[Python language]] for solving [[Nonlinear programming|NLP]], [[Linear programming|LP]], [[Integer programs|MIP]], [[quadratic programming|QP]], etc with [[automatic differentiation]] features.
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| |[[OptaPlanner]]||[[Apache_license|ASL]] || OptaPlanner is a lightweight, embeddable planning engine written in Java™. It helps normal Java™ programmers solve constraint satisfaction problems efficiently. Under the hood, it combines optimization heuristics and metaheuristics with very efficient score calculation.
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| |[http://bugseng.com/products/ppl PPL] || GPLv3 || integer programming problems, polyhedra
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| |[[Scilab]]||[[CeCILL]] || cross-platform numerical computational package and a high-level, numerically oriented programming language with free numerical optimization framework.
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| |[http://www.mcs.anl.gov/research/projects/tao/ TAO]|| [[BSD licenses | BSD]] || large-scale optimization, focus on parallel algos.
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| |}
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| ==Proprietary software==
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| *[[AIMMS]] — optimization modeling system, including GUI building facilities
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| *[[AMPL]] — modelling language for large-scale linear, mixed integer and nonlinear optimization
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| *[[APMonitor]] — for large-scale, nonlinear, differential and algebraic optimization
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| *[[ASTOS]] — AeroSpace Trajectory Optimization Software for launcher, re-entry and generic aerospace problems
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| *[[BARON]] — for global optimization of algebraic nonlinear and mixed-integer nonlinear problems
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| *[[CPLEX]] — integer, linear and quadratic programming
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| *[[FortMP]] — integer, linear and quadratic programming
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| *[[FortSP]] — stochastic programming
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| *[[General Algebraic Modeling System]]
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| *[[Gurobi]] — integer, linear and quadratic programming
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| *[http://berkutec.com/index.php/en HillStormer] — [[Nelder–Mead method|Nelder–Mead]] nonlinear optimization with linear constraints
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| *[[Red Cedar Technology#HEEDS MDO|HEEDS MDO]] — multidisciplinary design optimization using SHERPA, a hybrid, adaptive optimization algorithm.
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| *[[IMSL Numerical Libraries]] Linear, quadratic, nonlinear, and sparse QP and LP optimization algorithms implemented in standard programming languages C, Java, C# .NET, Fortran, and Python.
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| *[[IOSO]] — (Indirect Optimization on the basis of Self-Organization) is a multiobjective, multidimensional nonlinear optimization technology
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| *[[Kimeme]] — an open platform for multi-objective optimization and multidisciplinary design optimization
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| *[http://www.lindo.com/ Lingo] — Linear, integer, nonlinear and stochastic programming. Global optimization
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| *[[LIONsolver]] — an integrated software for data mining, modeling, ''Learning and Intelligent OptimizatioN'' and [[reactive business intelligence]]
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| *[[modeFRONTIER]] — multidisciplinary design optimization, for computer-aided engineering
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| *[[Maple (software)]] — Linear, quadratic, and nonlinear, continuous and integer optimization. Constrained and unconstrained. Global optimization with add-on toolbox.
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| *[[MATLAB]] — Linear, quadratic, and nonlinear problems with [[Optimization Toolbox]]; multiple maxima, multiple minima, and non-smooth optimization problems; estimation and optimization of model parameters.
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| *[[Mathematica]] — large-scale multivariate constrained and unconstrained, linear and nonlinear, continuous and integer optimization.
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| *[http://www.midaco-solver.com/ MIDACO] Global optimization software based on evolutionary computing, MINLP (Matlab, Octave, Python, C/C++ and Fortran)
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| *[[MOSEK]] — linear, quadratic, conic and convex nonlinear, continuous and integer optimization.
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| *[[NAG Numerical Library|NAG]] — Linear, quadratic, nonlinear, sums of squares of linear or nonlinear functions; linear, sparse linear, nonlinear, bounded or no constraints; local and global optimization; continuous or integer problems.
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| *[[Nexus (Process integration and optimization)|Nexus]] — multidisciplinary optimization and design process integration
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| *[[NMath]] — linear, quadratic and nonlinear programming
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| *[[IOSO]] — multidisciplinary design optimization, for computer-aided engineering
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| *[[OptimJ]] — Java based modeling language. Premium Edition includes support for Gurobi, Mosek and CPLEX solvers
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| *[[Optimus platform]] — a process integration and design optimization platform developed by Noesis Solutions
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| *[[OptiY]] - a design environment providing modern optimization strategies and state of the art probabilistic algorithms for uncertainty, reliability, robustness, sensitivity analysis, data-mining and meta-modeling.
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| *[[OptiStruct]] — Award-winning CAE technology for conceptual design synthesis and structural optimization.
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| *[[PHX ModelCenter]] — a graphical environment for automation, integration, and design optimization.
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| * [[PottersWheel]] — Parameter estimation in ordinary differential equations (Matlab toolbox, free for academic use).
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| *[[SmartDO]] — multidisciplinary global design optimization, specialized in computer-aided engineering (CAE). using the direct global search approaches.
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| *[[SNOPT]] — large-scale optimization problems.
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| *[[The Unscrambler|Unscrambler Optimizer]] product formulation and process optimization software
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| *[[TOMLAB]] — TOMLAB supports global optimization, integer programming, all types of least squares, linear, quadratic and unconstrained programming for [[MATLAB]]. TOMLAB supports solvers like [[Gurobi]], [[CPLEX]], [[SNOPT]] and [[KNITRO]].
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| *[[VisSim]] — a visual [[block diagram]] language for simulation and optimization of [[dynamical system]]s.
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| *[[WORHP]] — a large-scale sparse solver for continuous nonlinear optimization.
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| ===Freeware===
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| *[[AIMMS]] — free for academic use.
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| *[[AMPL]] — free student license.
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| *[[APMonitor]] — free for academic or commercial use with interfaces to Python and MATLAB.
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| *[[ASTOS]] — free for academic use.
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| *[[Galahad library]] — free for academic use.
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| *[[LIONsolver]] — free license for academic use.
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| *[http://www.midaco-solver.com/ MIDACO] Global optimization software based on evolutionary computing, MINLP (Matlab, Octave, Python, C/C++ and Fortran)
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| *[[MINTO]] — integer programming solver using branch and bound algorithm. Freeware for personal use.
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| *[[OptimJ]] — Java based modeling language. Free Edition includes support for lp_solve, GLPK and LP or MPS file formats
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| *[[PottersWheel]] — Parameter estimation in ordinary differential equations (Free Matlab toolbox for academic use).
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| *[[SCIP (optimization software)|SCIP]] — Free only for research purpose as a member of a non-commercial and academic institution.
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| *[[WORHP]] — free of charge for academic use.
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| ==See also==
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| * [[Comparison of optimization software]]
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| * [[List of numerical libraries]]
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| {{Mathematical optimization software}}
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| [[Category:Mathematical optimization software|*]]
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| [[Category:Lists of software|Optimization software]]
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