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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