Mathematical Programming with Increasing Constraint Functions

William P. Pierskalla
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William P. Pierskalla: Southern Methodist University

Management Science, 1969, vol. 15, issue 7, 416-425

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.

Date: 1969
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