This is documentation for Mathematica 9, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


Integrated into Mathematica is a full range of state-of-the-art local and global optimization techniques, both numeric and symbolic, including constrained nonlinear optimization, interior point methods and integer programming—as well as original symbolic methods. Mathematica's symbolic architecture provides seamless access to industrial-strength system and model optimization, efficiently handling million-variable linear programming, and multithousand-variable nonlinear problems.


Numerical Optimization

NMinimize, NMaximize nonlinear constrained global optimization

FindMinimum, FindMaximum local unconstrained or constrained optimization

FindFit optimal nonlinear unconstrained or constrained fit to data

Symbolic Optimization

Minimize, Maximize symbolic global optimization

Extremal Values & Locations

MinValue, MaxValue minimum, maximum values

NMinValue ▪ NMaxValue ▪ FindMinValue ▪ FindMaxValue

ArgMin, ArgMax position of minimum, maximum

NArgMin ▪ NArgMax ▪ FindArgMin ▪ FindArgMax

Matrix Forms

LinearProgramming real and integer linear programming in matrix form

LeastSquares least-squares problem in matrix form

Combinatorial Optimization »

FindShortestTour solve a traveling salesman problem

Minimize, FindMinimum solve integer programming problems

ArgMin, MinValue, ... — position, value of minima

Inequality Visualization

RegionPlot, RegionPlot3D plot regions satisfied by inequalities