Mathematical Programming with Increasing Constraint Functions

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.

• 저널Management Science · 15(7) · 416–425
• 토픽Optimization and Mathematical Programming · Control and Systems Engineering
• DOI10.1287/mnsc.15.7.416
• 저자William P. Pierskalla