Variants of the Ekeland Variational Principle for a set-valued map involving the Clarke Normal Cone
Copyright policy )Variants of the Ekeland Variational Principle for a set-valued map involving the Clarke Normal Cone
In this paper it is extended Ekeland's variational principle to vector-set-valued maps \(F\). The author uses the Clarke normal cone of the graph of \(F\), which enables him to establish sufficient conditions on \(F\) in order to have a weak minimizer or a properly positive minimizer when the Palais-Smale compactness condition is fulfilled. The proof of the main result is based on the Clarke-Rockafellar theorem on the generalized gradient of a sum of nonsmooth functions.
- Institute of Mathematics Viet Nam
coderivative, vector optimization, set-valued map, Applied Mathematics, Nonsmooth analysis, Ekeland's variational principle, Set-valued map, Ekeland variational principle, Optimality conditions for problems in abstract spaces, Clarke normal cone, Clarke's normal cone, Vector optimization, Coderivative, Multi-objective and goal programming, Analysis, Set-valued and variational analysis
coderivative, vector optimization, set-valued map, Applied Mathematics, Nonsmooth analysis, Ekeland's variational principle, Set-valued map, Ekeland variational principle, Optimality conditions for problems in abstract spaces, Clarke normal cone, Clarke's normal cone, Vector optimization, Coderivative, Multi-objective and goal programming, Analysis, Set-valued and variational analysis
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