A simple approach to optimality conditions in minmax programming

摘要

Considering the minmax programming problem, lower and upper subdifferential optimality conditions, in the sense of Mordukhovich, are derived. The approach here, mainly based on the nonsmooth dual objects of Mordukhovich, is completely different from that of most of the previous works where generalizations of the alternative theorem of Farkas have been applied. The results obtained are close to those known in the literature. However, one of the main achievements of this article is that we could also derive necessary optimality conditions for the minmax program of the usual Karush-Kuhn-Tucker type, which seems to be new in this field of study.