Abstract
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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Work of the first author was supported by DAAD (Deutscher Akademischer Austausch Dienst) with a scholarship grant.
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Mersha, A.G., Dempe, S. Direct search algorithm for bilevel programming problems. Comput Optim Appl 49, 1–15 (2011). https://doi.org/10.1007/s10589-009-9295-9
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DOI: https://doi.org/10.1007/s10589-009-9295-9