Sequential approximate weak optimality conditions for multiobjective fractional programming problems via sequential calculus rules for the Brøndsted-Rockafellar approximate subdifferential

Abstract

In this paper, in the absence of any constraint qualifications, we develop sequential necessary and sufficient optimality conditions for a constrained multiobjective fractional programming problem characterizing a Henig proper efficient solution in terms of the ǫ-subdifferentials and the subdifferentials of the functions. This is achieved by employing a sequential Henig subdifferential calculus rule of the sums of m (m ≥ 2) proper convex vector valued mappings with a composition of two convex vector valued mappings. In order to present an example illustrating the main results of this paper, we establish the classical optimality conditions under Moreau-Rockafellar qualification condition. Our main results are presented in the setting of reflexive Banach space in order to avoid the use of nets.