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.
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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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Ha, T.X.D. Some Variants of the Ekeland Variational Principle for a Set-Valued Map. J Optim Theory Appl 124, 187–206 (2005). https://doi.org/10.1007/s10957-004-6472-y
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DOI: https://doi.org/10.1007/s10957-004-6472-y