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×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. Mathematics Subject Classification (2010): 47H05, 47H04, 49J53, 90C33.

Bianchi, M., Hadjisavvas, N., Pini, R. (2022). Continuity and maximal quasimonotonicity of normal cone operators. STUDIA UNIVERSITATIS BABES-BOLYAI. MATHEMATICA, 67(1), 31-45 [10.24193/subbmath.2022.1.03].

Continuity and maximal quasimonotonicity of normal cone operators

Pini, R
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×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. Mathematics Subject Classification (2010): 47H05, 47H04, 49J53, 90C33.
Articolo in rivista - Articolo scientifico
Cone upper semicontinuity; Maximal quasimonotone operator; Quasiconvex function; Quasimonotone operator; Upper sign continuity;
English
2022
67
1
31
45
none
Bianchi, M., Hadjisavvas, N., Pini, R. (2022). Continuity and maximal quasimonotonicity of normal cone operators. STUDIA UNIVERSITATIS BABES-BOLYAI. MATHEMATICA, 67(1), 31-45 [10.24193/subbmath.2022.1.03].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/363978
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