Pareto subdifferential calculus for convex set-valued mappings and applications to set optimization

This paper provides an extension of a recent work by El Maghri and Laghdir, 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 the 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 regular subdifferentiability.Some applications to a general set-valued optimization problem are given to illustrate our main results.