Farkas Type Theorems For Generalized Convexities

摘要

In this paper are proved Farkas' theorems for Konig convex functions (inequalityconstraints) and Ky Fan convex-linear functions (inequality and equality constraints). Necessary optimality conditions for Konig/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. (Copyright (c) 1994 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)