mathematical programming
mathematical programming A wide field of study that deals with the theory, applications, and computational methods for optimization problems. An abstract formulation of such problems is to maximize a function f (known as an objective function) over a constraint set S, i.e. maximize f(x), x ∈ S ⊆ R^{n},
where R^{n} denotes the space of real ncomponent vectors x, x = (x_{1},x_{2},…,x_{n})^{T}
and f is a realvalued function defined on S. If S consists only of vectors whose elements are integers, then the problem is one of integer programming. Linear programming treats the case of f as a linear function with S defined by linear equations and/or constraints. Nonlinear objective functions with or without constraints (defined by systems of nonlinear equations) give rise to problems generally referred to as optimization problems.
Mathematicalprogramming problems arise in engineering, business, and the physical and social sciences.
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