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.
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Daniilidis, A., Garcia Ramos, Y. Some Remarks on the Class of Continuous (Semi-) Strictly Quasiconvex Functions. J Optim Theory Appl 133, 37–48 (2007). https://doi.org/10.1007/s10957-007-9182-4
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DOI: https://doi.org/10.1007/s10957-007-9182-4