Continuity and maximal quasimonotonicity of normal cone operators

Monica Bianchi; Nicolas Hadjisavvas; Rita Pini

doi:10.24193/subbmath.2022.1.03

Authors

Monica Bianchi
Nicolas Hadjisavvas
Rita Pini http://orcid.org/0000-0002-5843-6814

DOI:

https://doi.org/10.24193/subbmath.2022.1.03

Keywords:

quasimonotone operator, maximal quasimonotone operator, cone upper semicontinuity, upper sign continuity, quasiconvex function

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 $s\times w^*$ cone upper semicontinuity of the normal cone operator in the domain of $f$ in case the set of global minima has non empty interior.

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