Pareto epsilon-subdifferential sum rule for set-valued mappings and applications to set optimization

In this paper, we are mainly concerned with a rule for efficient (Pareto) approximate subdifferential, concerning the sum of two cone-convex set-valued vector mappings, taking values in finite or infinite-dimensional preordred spaces. The obtained formula is exact and holds under the connectedness or Attouch-Brézis qualification conditions and the regular subdifferentiability. This formula is applied to establish approximate necessary and sufficient optimality conditions for the existence of the approximate Pareto (weak or proper) efficient solutions of a set-valued vector optimization problem.