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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 programming—as 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 OptimizationNMinimize, NMaximize — nonlinear constrained global optimization
FindMinimum, FindMaximum — local unconstrained or constrained optimization
FindFit — optimal nonlinear unconstrained or constrained fit to data
Symbolic OptimizationMinimize, Maximize — symbolic global optimization
Extremal Values & LocationsMinValue, MaxValue — minimum, maximum values
NMinValue ▪ NMaxValue ▪ FindMinValue ▪ FindMaxValue
ArgMin, ArgMax — position of minimum, maximum
NArgMin ▪ NArgMax ▪ FindArgMin ▪ FindArgMax
Matrix FormsLinearOptimization — 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 0–1 knapsack problems
FrobeniusSolve — mixed radix constraint satisfaction (e.g. coin changing) problems
Generalized OptimizationBayesianMinimization — model-based minimization of numeric, text, image, ... functions
BayesianMinimizationObject — representation of the result of model-based minimization
BayesianMaximization ▪ BayesianMaximizationObject
Inequality VisualizationRegionPlot, RegionPlot3D — plot regions satisfied by inequalities
Special CasesNetTrain — train a neural net with a specified loss function
SpherePoints — equally spaced points on a sphere
EstimatedDistribution ▪ EstimatedProcess ▪ FindFormula ▪ ...
FindGeometricTransform ▪ ImageAlign ▪ GuidedFilter ▪ ...
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