Sequential Henig proper optimality conditions for multiobjective fractional programming problems via sequential proper subdifferential calculus

TL;DR

This paper develops sequential optimality conditions for multiobjective fractional programming problems without constraint qualifications, using advanced subdifferential calculus in reflexive Banach spaces.

Contribution

It introduces new sequential necessary and sufficient optimality conditions for constrained multiobjective fractional problems utilizing Henig proper subdifferentials without constraint qualifications.

Findings

Established sequential optimality conditions in reflexive Banach spaces.

Derived classical optimality conditions under Moreau-Rockafellar qualification.

Applied subdifferential calculus to multiobjective fractional programming.

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 $\epsilon$-subdifferentials and the subdifferentials of the functions. This is achieved by employing a sequential Henig subdifferential calculus rule of the sums of $m \ (m\geq 2)$ 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.