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.
|Number of pages||12|
|Journal||Reports of the Faculty of Technical Mathematics and Informatics|
|Publication status||Published - 1 Jan 1994|
- Farkas type theorems