Continuity and maximal quasimonotonicity of normal cone operators.

Abstract:  In this talk we present 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 that appeared recently in the literature, and we show that this operator is maximal quasimonotone in this sense. Among other results, we prove
the $s\times w^{\ast}$ cone upper semicontinuity of the normal cone operator in the domain of $f$, in case the set of global minima is empty, or a singleton, or has non empty interior (joint work with M. Bianchi and R. Pini).