TY - JOUR
T1 - Continuity and maximal quasimonotonocity of normal cone operators
AU - Bianchi, Monica
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Quasimonotone operator
KW - cone upper semicontinuity
KW - maximal quasimonotone operators
KW - Quasimonotone operator
KW - cone upper semicontinuity
KW - maximal quasimonotone operators
UR - http://hdl.handle.net/10807/197038
U2 - 10.24193/subbmath.2022.1.03
DO - 10.24193/subbmath.2022.1.03
M3 - Article
SN - 0252-1938
VL - 2022
SP - 31
EP - 45
JO - STUDIA UNIVERSITATIS BABES-BOLYAI. MATHEMATICA
JF - STUDIA UNIVERSITATIS BABES-BOLYAI. MATHEMATICA
ER -