Illés, T.; Kassay, G. Farkas type theorems for generalized convexities. (English) Zbl 0821.90091 PU.M.A., Pure Math. Appl. 5, No. 2, 225-239 (1994). 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. Cited in 7 Documents MSC: 90C25 Convex programming Keywords:necessary optimality conditions; generalized convexities PDF BibTeX XML Cite \textit{T. Illés} and \textit{G. Kassay}, PU.M.A., Pure Math. Appl. 5, No. 2, 225--239 (1994; Zbl 0821.90091) OpenURL