In this paper we study some properties of the adjusted normal cone operator of quasiconvex functions. In particular, we introduce a new notion of maximal quasimotonicity for set-valued maps different from similar ones recently appeared in the literature, and we show that it is enjoyed by this operator. Moreover, we prove the s x w* cone upper semicontinuity of the normal cone operator in the domain of $f$ in case the set of global minima has non empty interior.
Bianchi, M., Pini, R., Hadjisavvas, N., Continuity and maximal quasimonotonocity of normal cone operators, <<STUDIA UNIVERSITATIS BABES-BOLYAI. MATHEMATICA>>, 2022; 2022 (1): 31-45. [doi:10.24193/subbmath.2022.1.03] [http://hdl.handle.net/10807/197038]
Continuity and maximal quasimonotonocity of normal cone operators
Bianchi, Monica;
2022
Abstract
In this paper we study some properties of the adjusted normal cone operator of quasiconvex functions. In particular, we introduce a new notion of maximal quasimotonicity for set-valued maps different from similar ones recently appeared in the literature, and we show that it is enjoyed by this operator. Moreover, we prove the s x w* cone upper semicontinuity of the normal cone operator in the domain of $f$ in case the set of global minima has non empty interior.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.