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A SIMPLE APPROACH TO OPTIMALITY CONDITIONS IN MINMAX PROGRAMMING

Alain B. Zemkoho (zemkoho***at***daad-alumni.de)

Abstract: Considering the minmax programming problem, lower and upper subdi erential optimality conditions, in the sense of Mordukhovich, are derived. The approach here, mainly based on the nonsmooth dual objects of Mordukhovich, is completely di erent 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.

Keywords: minmax programming; optimal value function; optimality conditions; inner semicom- pact/semicontinuous set-valued mapping; convexity

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Nonlinear Optimization

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Alain B. Zemkoho. A simple approach to optimality conditions in minmax programming. Optimization (2012). doi: 10.1080/02331934.2011.653788

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Entry Submitted: 10/28/2011
Entry Accepted: 10/28/2011
Entry Last Modified: 02/01/2012

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