TY - JOUR
T1 - Some remarks on the class of continuous (semi-)∈strictly quasiconvex functions
AU - Daniilidis, A.
AU - Ramos, Y. Garcia
PY - 2007/4/1
Y1 - 2007/4/1
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.
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.
KW - Quasiconvex functions
KW - Quasimonotone operators
KW - Utility functions
KW - Variational analysis
KW - Quasiconvex functions
KW - Quasimonotone operators
KW - Utility functions
KW - Variational analysis
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U2 - 10.1007/s10957-007-9182-4
DO - 10.1007/s10957-007-9182-4
M3 - Article in a journal
SN - 0022-3239
VL - 133
SP - 37
EP - 48
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 1
ER -