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 |
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Pages (from-to) | 37-48 |
Journal | Journal of Optimization Theory and Applications |
Volume | 133 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Apr 2007 |
Keywords
- Quasiconvex functions
- Quasimonotone operators
- Utility functions
- Variational analysis