TY - JOUR
T1 - Closedness under addition for families of quasimonotone operators
AU - Flores-Bazán, Fabián
AU - Hadjisavvas, Nicolas
AU - García-Ramos, Yboon
N1 - eISSN: 1029-4945
Publisher Copyright: © 2022 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2022/12/7
Y1 - 2022/12/7
N2 - In the last two decades, several properties of operators that
are weaker than monotonicity have received attention by researchers from many
areas including mathematical economics, with the goal to develop new tools
applicable in convex analysis and related topics. This paper puts in
perspective notions that are extensions of monotoniticity but not beyond
quasimonotonicity like pseudomonotonicity, semistrict quasimonotonicity, strict
quasimonotonicity and proper quasimonotonicity, and discusses systematically
when the sum of two operators satisfying one of those properties, inherits the
same property. The case of properly quasimonotone operators deserves a special
attention since this notion, being stronger than quasimonotonicity, suffices to
obtain many results, including the solvability of variational inequality
problems. Several examples showing the optimality in some sense of our results,
are presented.
AB - In the last two decades, several properties of operators that
are weaker than monotonicity have received attention by researchers from many
areas including mathematical economics, with the goal to develop new tools
applicable in convex analysis and related topics. This paper puts in
perspective notions that are extensions of monotoniticity but not beyond
quasimonotonicity like pseudomonotonicity, semistrict quasimonotonicity, strict
quasimonotonicity and proper quasimonotonicity, and discusses systematically
when the sum of two operators satisfying one of those properties, inherits the
same property. The case of properly quasimonotone operators deserves a special
attention since this notion, being stronger than quasimonotonicity, suffices to
obtain many results, including the solvability of variational inequality
problems. Several examples showing the optimality in some sense of our results,
are presented.
KW - Quasiconvex function
KW - quasiconvex optimization
KW - quasimonotone operator
KW - Quasiconvex function
KW - Quasimonotone operator
KW - Quasiconvex optimization
UR - http://www.scopus.com/inward/record.url?scp=85144029821&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/b7992c34-570a-331c-a622-bd4b549f8151/
U2 - 10.1080/02331934.2022.2154127
DO - 10.1080/02331934.2022.2154127
M3 - Artículo de revista
AN - SCOPUS:85144029821
SN - 0233-1934
JO - Optimization
JF - Optimization
ER -