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Erschienen in:
2015 | OriginalPaper | Buchkapitel
4. Convex Bilevel Programs
verfasst von : Stephan Dempe, Vyacheslav Kalashnikov, Gerardo A. Pérez-Valdés, Nataliya Kalashnykova
Erschienen in: Bilevel Programming Problems
Verlag: Springer Berlin Heidelberg
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Abstract
The task to find a best point within the set of optimal solutions of a convex optimization problem is called simple bilevel optimization problem. In general, a necessary optimality condition for a convex simple bilevel problem does not need to be sufficient. An adapted necessary and sufficient optimality condition is derived using tools from cone-convex optimization and a gradient type descent method is suggested which combines the use of a convex combination of both objective functions and projection onto the feasible set. In the second section, a similar algorithm is used to find a best point within the solutions of a variational inequality.