Journal
SET-VALUED AND VARIATIONAL ANALYSIS
Volume 25, Issue 1, Pages 113-132Publisher
SPRINGER
DOI: 10.1007/s11228-016-0369-4
Keywords
Bilevel optimization; Convergence of multifunctions; Marginal functions; Variational-convergence; Convex analysis
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The paper deals with a strong-weak nonlinear bilevel problem which generalizes the well-known weak and strong ones. In general, the study of the existence of solutions to such a problem is a difficult task. So that, for a strong-weak nonlinear bilevel problem, we first give a regularization based on the use of strict oee--solutions of the lower level problem. Then, via this regularization and under sufficient conditions, we show that the problem admits at least one solution. The obtained result is an extension and an improvement of some recent results appeared recently in the literature for both weak nonlinear bilevel programming problems and linear finite dimensional case.
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