Considering the minmax programming problem, lower and upper subdierential optimality conditions, in the sense of Mordukhovich, are derived. The approach here, mainly based on the nonsmooth dual objects of Mordukhovich, is completely dierent from that of most of the previous works where generalizations of the alternative theorem of Farkas have been applied. The results obtained are closed to those known in the literature. However, one of the main achieve- ments of the paper 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 eld of study.
Alain B. Zemkoho. A simple approach to optimality conditions in minmax programming. Optimization (2012). doi: 10.1080/02331934.2011.653788