Some remarks on the class of continuous (semi-)∈strictly quasiconvex functions

A. Daniilidis, Y. Garcia Ramos

Research output: Contribution to journalArticle in a journalpeer-review

12 Scopus citations


We introduce the notion of variational (semi-)∈strict quasimonotonicity for a multivalued operator T ∈: X * relative to a nonempty subset A of X which is not necessarily included in the domain of T. We use this notion to characterize the subdifferentials of continuous (semi-)∈strictly quasiconvex functions. The proposed definition is a relaxation of the standard definition of (semi-)∈strict quasimonotonicity, the latter being appropriate only for operators with nonempty values. Thus, the derived results are extensions to the continuous case of the corresponding results for locally Lipschitz functions.
Original languageEnglish
Pages (from-to)37-48
Number of pages12
JournalJournal of Optimization Theory and Applications
Issue number1
StatePublished - 1 Apr 2007
Externally publishedYes


  • Quasiconvex functions
  • Quasimonotone operators
  • Utility functions
  • Variational analysis


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