This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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Optimization
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
ArgMin, ArgMax position of minimum, maximum
Matrix Forms
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
ArgMin, MinValue, ... — position, value of minima

Inequality Visualization
RegionPlot, RegionPlot3D plot regions satisfied by inequalities
TUTORIALS
TUTORIAL COLLECTION