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.
scientific article; zbMATH DE number 5016184