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.
Inglese
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/197038
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