On semi-infinite minmax programming with generalized invexity. (English) Zbl 1282.90206

Summary: Here, we consider the minmax programming problem with a set of restrictions indexed in a compact. As a novelty, we obtain optimality criteria of the Kuhn-Tucker type involving a limited number of restrictions and prove both necessity and sufficiency under new weaker invexity assumptions. Also some dual problems are introduced and it is proved that the weak and strong duality properties hold within the same environment.


90C34 Semi-infinite programming
90C47 Minimax problems in mathematical programming
90C46 Optimality conditions and duality in mathematical programming
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