Optimization

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 Optimization

(RefLink[NMinimize, paclet:ref/NMinimize]), (RefLink[NMaximize, paclet:ref/NMaximize]) — nonlinear constrained global optimization

(RefLink[FindMinimum, paclet:ref/FindMinimum]), (RefLink[FindMaximum, paclet:ref/FindMaximum]) — local unconstrained or constrained optimization

(RefLink[FindFit, paclet:ref/FindFit]) — optimal nonlinear unconstrained or constrained fit to data

Symbolic Optimization

(RefLink[Minimize, paclet:ref/Minimize]), (RefLink[Maximize, paclet:ref/Maximize]) — symbolic global optimization

Extremal Values & Locations

(RefLink[MinValue, paclet:ref/MinValue]), (RefLink[MaxValue, paclet:ref/MaxValue]) — minimum, maximum values

(RefLink[ArgMin, paclet:ref/ArgMin]), (RefLink[ArgMax, paclet:ref/ArgMax]) — position of minimum, maximum

Matrix Forms

(RefLink[LinearProgramming, paclet:ref/LinearProgramming]) — real and integer linear programming in matrix form

(RefLink[LeastSquares, paclet:ref/LeastSquares]) — least-squares problem in matrix form

(OrangeLink[Convex Optimization », paclet:guide/ConvexOptimization])

(RefLink[LinearOptimization, paclet:ref/LinearOptimization]) — minimize {c.x|a.x+b \[VectorGreaterEqual]0}

(RefLink[LinearFractionalOptimization, paclet:ref/LinearFractionalOptimization]) — minimize {(α.x+β)/(γ.x+δ)|a.x+b\[VectorGreaterEqual]0}

(RefLink[QuadraticOptimization, paclet:ref/QuadraticOptimization]) — minimize {(1/2)x.q.x+c.x|a.x+b\[VectorGreaterEqual]0}

(RefLink[SecondOrderConeOptimization, paclet:ref/SecondOrderConeOptimization]) — minimize {c.x|‖(Subscript[a, j]).x+(Subscript[b, j])‖≤(Subscript[α, j])+(Subscript[β, j]),j=1… k}

(RefLink[SemidefiniteOptimization, paclet:ref/SemidefiniteOptimization]) — minimize {c.x|(Subscript[a, 0])+(Subscript[x, 1])(Subscript[a, 1])+…+(Subscript[x, k])(Subscript[a, k])(Subscript[\[VectorGreaterEqual], (Subscript[𝒮, +]^n)])0}

(RefLink[ConicOptimization, paclet:ref/ConicOptimization]) — minimize {c.x|(Subscript[a, j]).x+(Subscript[b, j])(Subscript[\[VectorGreaterEqual], (Subscript[κ, j])])0, j=1… k}

(OrangeLink[Combinatorial Optimization », paclet:guide/DiscreteMathematics])

(RefLink[FindShortestTour, paclet:ref/FindShortestTour]) — solve a traveling salesman problem

(RefLink[Minimize, paclet:ref/Minimize]), (RefLink[FindMinimum, paclet:ref/FindMinimum]) — solve integer programming problems

(RefLink[ArgMin, paclet:ref/ArgMin]), (RefLink[MinValue, paclet:ref/MinValue]), … — position, value of minima

(RefLink[KnapsackSolve, paclet:ref/KnapsackSolve]) — solve bounded, unbounded and 0–1 knapsack problems

(RefLink[FrobeniusSolve, paclet:ref/FrobeniusSolve]) — mixed radix constraint satisfaction (e.g. coin changing) problems

Generalized Optimization

(RefLink[BayesianMinimization, paclet:ref/BayesianMinimization]) — model-based minimization of numeric, text, image, ... functions

(RefLink[BayesianMinimizationObject, paclet:ref/BayesianMinimizationObject]) — representation of the result of model-based minimization

Inequality Visualization

(RefLink[RegionPlot, paclet:ref/RegionPlot]), (RefLink[RegionPlot3D, paclet:ref/RegionPlot3D]) — plot regions satisfied by inequalities

Special Cases

(RefLink[NetTrain, paclet:ref/NetTrain]) — train a neural net with a specified loss function

(RefLink[SpherePoints, paclet:ref/SpherePoints]) — equally spaced points on a sphere