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The Ekeland variational principle for set-valued maps involving coderivatives. (English) Zbl 1029.49018

Summary: We use the Fréchet, Clarke, and Mordukhovich coderivatives to obtain variants of the Ekeland variational principle for a set-valued map \(F\) and establish optimality conditions for set-valued optimization problems. Our technique is based on scalarization with the help of a marginal function associated with \(F\) and estimates of subdifferentials of this function in terms of coderivatives of \(F\).

MSC:

49J53 Set-valued and variational analysis
49J52 Nonsmooth analysis
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