Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1-12 |
| Number of pages | 12 |
| Journal | Reports of the Faculty of Technical Mathematics and Informatics |
| Volume | 94 |
| Issue number | 23 |
| Publication status | Published - 1 Jan 1994 |
Keywords
- Farkas type theorems
- convexities