Some Variants of the Ekeland Variational Principle for a Set-Valued Map Article DOI:
Cite this article as: Ha, T.X.D. J Optim Theory Appl (2005) 124: 187. doi:10.1007/s10957-004-6472-y Abstract
This paper deals with the Ekeland variational principle (EVP) for a set-valued map F with values in a vector space
E. Using the concept of cone extension and the Mordukhovich coderivative, we formulate some variants of the EVP for F under various continuity assumptions. We investigate also the stability of a set-valued EVP. Our approach is motivated by the set approach proposed by Kuroiwa for minimizing set-valued maps. Keywords Ekeland variational principle set-valued maps Mordukhovich coderivatives stability
This research was supported by a Georg Forster Grant administered by the Alexander von Humboldt Foundation. The author thanks Professor J. Jahn, University of
Erlangen-Nürnberg, for comments on the manuscript. The author thanks the referee for suggestions which improved the paper.
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