Research Communication | Open Access
Volume 2021 | Communication ID 47
Volume 2021 | Communication ID 47
| Pareto subdifferential calculus for convex set-valued mappings and applications to set optimization |
Echchaabaoui El Mahjoub, Laghdir Mohamed, Moustaid Mohamed Bilal
Received |
Accepted |
Published |
January 23, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: This paper provides an extension of a recent work by El Maghri and Laghdir [1], dealing with the subdifferential calculus for convex vector mappings. The purpose of this paper is to study the Pareto subdifferential (weak and proper) for convex set-valued mappings defined via Pareto efficiency, from a point of view of characterizations and calculus rules. We develop calculus rules of the Pareto subdifferentials for the sum and/or composition of two convex set-valued mappings. The obtained formulas are original and hold under the weak conditions of the connectedness or Attouch-Brézis and the ...