| Article ID: | iaor2012619 |
| Volume: | 152 |
| Issue: | 3 |
| Start Page Number: | 661 |
| End Page Number: | 674 |
| Publication Date: | Mar 2012 |
| Journal: | Journal of Optimization Theory and Applications |
| Authors: | Capata Adela |
| Keywords: | duality, Programming (cone), vector optimization, inequality problems |
The purpose of this paper is to establish necessary and sufficient conditions for a point to be solution of an extended Ky Fan inequality. Using a separation theorem for convex sets, involving the quasi‐interior of a convex set, we obtain optimality conditions for solutions of the generalized problem with cone and affine constraints. Then the main result is applied to vector optimization problems with cone and affine constraints and to duality theory.