INTRODUCTION AND PERSPECTIVE
Nonlinear programming [a term coined by Kuhn and Tucker (Kuhn, 1991)] has come to mean that collection of methodology associated with any optimization problem where nonlinear relationships may be present in the objective function or the constraints. Since maximization and minimization are mathematically equivalent, without loss of generality we shall assume that the nonlinear programming problem is the problem of finding a solution point or optimal value of
where all problem functions are real valued. The underlying space can be more general, but here we shall assume xv ∈ E n, the well known Euclidian n-space. In this terminology and context, problem (P) is a linear program (LP) if f, g i and h j are linear (actually linear-affine, i.e., linear plus a constant) for all i and j.
Another very important instance of problem (P) is where the constraints g i and h j are not present or where every point in the domain of fis feasible (i.e., satisfies the...
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Fiacco, A.V. (2001). Nonlinear programming . In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_682
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