Integrated into the Wolfram Language 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 programmingas well as original symbolic methods. The Wolfram Language'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

LinearOptimization real and integer linear programming in matrix form

LeastSquares least-squares problem in matrix form

Convex Optimization »

ConvexOptimization minimize with convex

ParametricConvexOptimization minimize with parameters

RobustConvexOptimization minimize with uncertainties

LinearOptimization  ▪  LinearFractionalOptimization  ▪  QuadraticOptimization  ▪  SecondOrderConeOptimization  ▪  SemidefiniteOptimization  ▪  ConicOptimization

Combinatorial Optimization »

FindShortestTour solve a traveling salesman problem

Minimize, FindMinimum solve integer programming problems

ArgMin, MinValue, position, value of minima

KnapsackSolve solve bounded, unbounded and 01 knapsack problems

FrobeniusSolve mixed radix constraint satisfaction (e.g. coin changing) problems

Generalized Optimization

BayesianMinimization model-based minimization of numeric, text, image, ... functions

BayesianMinimizationObject representation of the result of model-based minimization

BayesianMaximization  ▪  BayesianMaximizationObject

Inequality Visualization

RegionPlot, RegionPlot3D plot regions satisfied by inequalities

Special Cases

NetTrain train a neural net with a specified loss function

SpherePoints equally spaced points on a sphere

EstimatedDistribution  ▪  EstimatedProcess  ▪  FindFormula  ▪  ...

FindGeometricTransform  ▪  ImageAlign  ▪  GuidedFilter  ▪  ...