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Numerical algorithms for constrained nonlinear optimization can be broadly categorized into gradient-based methods and direct search methods. Gradient search methods use first derivatives (gradients) or second derivatives (Hessians) information. Examples are the sequential quadratic programming (SQP) method, the augmented Lagrangian method, and the (nonlinear) interior point method. Direct search methods do not use derivative information. Examples are Nelder|Mead, genetic algorithm and differential evolution, and ...

Constrained optimization problems are problems for which a function f (x) is to be minimized or maximized subject to constraints ? (x) . Here f : Rn ? R is called the objective function and F(x) is a Boolean-valued formula. In Mathematica the constraints ? (x) can be an arbitrary Boolean combination of equations g (x) ?0 , weak inequalities g (x) >=0, strict inequalities g(x)> 0, x is integer and x>0 statements. A point u ? Rn is said to be a global minimum of f subject to constraints F if u satisfies the constrai...

Linear programming problems are optimization problems where the objective function and constraints are all linear. Mathematica has a collection of algorithms for solving linear optimization problems with real variables, accessed via LinearProgramming, FindMinimum, FindMaximum, NMinimize, NMaximize, Minimize, and Maximize. LinearProgramming gives direct access to linear program- ming algorithms, provides the most flexibility for specifying the methods used, and is the most efficient for large-scale problems. FindMi...