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

A. Daniilidis; Y. Garcia Ramos

doi:10.1007/s10957-007-9182-4

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

A. Daniilidis, Y. Garcia Ramos

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

12 Citations (Scopus)

Abstract

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. © 2007 Springer Science+Business Media, LLC.

Original language	English
Pages (from-to)	37-48
Journal	Journal of Optimization Theory and Applications
Volume	133
Issue number	1
DOIs	https://doi.org/10.1007/s10957-007-9182-4
Publication status	Published - 1 Apr 2007

Keywords

Quasiconvex functions
Quasimonotone operators
Utility functions
Variational analysis

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abstract = "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. {\textcopyright} 2007 Springer Science+Business Media, LLC.",

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N2 - 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. © 2007 Springer Science+Business Media, LLC.

AB - 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. © 2007 Springer Science+Business Media, LLC.

KW - Quasiconvex functions

KW - Quasimonotone operators

KW - Utility functions

KW - Variational analysis

U2 - 10.1007/s10957-007-9182-4

DO - 10.1007/s10957-007-9182-4

M3 - Article

VL - 133

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EP - 48

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

SN - 0022-3239

IS - 1

ER -