Journal
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
Volume 49, Issue 1, Pages 1-15Publisher
SPRINGER
DOI: 10.1007/s10589-009-9295-9
Keywords
Bilevel programming; Nonsmooth optimization; Solution algorithm; Direct search algorithm; Clarke stationary solution
Funding
- DAAD (Deutscher Akademischer Austausch Dienst)
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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.
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