Some Remarks on the Class of Continuous (Semi-) Strictly Quasiconvex Functions

A. Daniilidis () and Y. Garcia Ramos ()
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A. Daniilidis: Universitat Autònoma de Barcelona
Y. Garcia Ramos: Université des Antilles et de la Guyane

Journal of Optimization Theory and Applications, 2007, vol. 133, issue 1, No 3, 37-48

Abstract: Abstract We introduce the notion of variational (semi-) strict quasimonotonicity for a multivalued operator T : X⇉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.

Keywords: Quasiconvex functions; Quasimonotone operators; Variational analysis; Utility functions (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-007-9182-4

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