where Rn denotes the space of real n-component vectors x, x = (x1,x2,…,xn)T
and f is a real-valued 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.
Mathematical-programming problems arise in engineering, business, and the physical and social sciences.
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