| Article ID: | iaor20114901 |
| Volume: | 49 |
| Issue: | 1 |
| Start Page Number: | 1 |
| End Page Number: | 15 |
| Publication Date: | May 2011 |
| Journal: | Computational Optimization and Applications |
| Authors: | Dempe Stephan, Mersha Getachew |
| Keywords: | heuristics, heuristics: local search, search |
In this paper, we study the application of a class of direct search methods to bilevel programming with convex lower level problems with strongly stable optimal solutions. In those methods, directions of descent in each iterations are selected within a finite set of directions. To guarantee the existence of such a finite set, we investigate the relation between the aperture of a descent cone at a non stationary point and the vector density of a finite set of directions. It is shown that the direct search method converges to a Clarke stationary point of the bilevel programming problem.