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2 results on '"quasimonotone operator"'

1. Continuity and maximal quasimonotonocity of normal cone operators

Author

Bianchi, Monica, Pini, Rita, Hadjisavvas, Nicolas, Bianchi Monica (ORCID:0000-0002-5296-3111), Bianchi, Monica, Pini, Rita, Hadjisavvas, Nicolas, and Bianchi Monica (ORCID:0000-0002-5296-3111)

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.

Published
2022

2. Continuity and maximal quasimonotonicity of normal cone operators

Author

Bianchi, M, Hadjisavvas, N, Pini, R, Bianchi, M, Hadjisavvas, N, and Pini, R

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.

Published
2022

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