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Farkas type theorems for generalized convexities. (English) Zbl 0821.90091

Summary: We prove Farkas’ theorems for König convex functions (inequality constraints) and Ky Fan convex-linear functions (inequality and equality constraints). Necessary optimality conditions for König/Ky Fan convex programming problems are given. Our results contain, in particular some results of Hayashi-Komiya, Simons and Zalinescu. Based on our statements and counterexamples we discuss the connections between different kinds of generalized convexities.

MSC:

90C25 Convex programming
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