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Mathematical Programming with Increasing Constraint Functions

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  • William P. Pierskalla

    (Southern Methodist University)

Abstract

The mathematical programming problem--find a non-negative n-vector x which maximizes f(x) subject to the constraints g i (x) > O, i - 1,..., m--is investigated where f(x) is assumed to be concave or pseudo-concave and the g i (x) are increasing functions. It is shown that under certain conditions on g i (x), the Kuhn-Tucker-Lagrange conditions are necessary and sufficient for the optimality of x*. It is also shown that the g i (x) are a useful class of functions since, among other properties, they are closed under non-negative addition, under the addition of any scalar, and under multiplication of non-negative members of the class. Examples of the above programming problem with increasing constraint functions are found in many chance-constrained programming problems.

Suggested Citation

  • William P. Pierskalla, 1969. "Mathematical Programming with Increasing Constraint Functions," Management Science, INFORMS, vol. 15(7), pages 416-425, March.
    • Handle: RePEc:inm:ormnsc:v:15:y:1969:i:7:p:416-425
    DOI: 10.1287/mnsc.15.7.416
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