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Integrated into Mathematica are 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 multi-thousand-variable nonlinear problems.
NMinimize, NMaximize nonlinear constrained global optimization
FindMinimum, FindMaximum local unconstrained or constrained optimization
FindFit optimal nonlinear unconstrained or constrained fit to data
Minimize, Maximize symbolic global optimization
RegionPlot, RegionPlot3D plot regions satisfied by inequalities
LinearProgramming real and integer linear programming in matrix form
LeastSquares least-squares problem in matrix form
FindShortestTour solve a traveling salesman problem
Minimize, FindMinimum solve integer programming problems