Optimality conditions and duality relations in nonsmooth fractional interval-valued multiobjective optimization

TL;DR

This paper develops optimality conditions and duality relations for nonsmooth fractional interval-valued multiobjective optimization problems, expanding the theoretical framework for such complex models using advanced variational analysis tools.

Contribution

It introduces four types of Pareto solutions, establishes necessary and sufficient optimality conditions, and formulates a dual model with duality relations for nonsmooth fractional interval-valued multiobjective problems.

Findings

Necessary optimality conditions derived using variational analysis.

Sufficient conditions established via generalized convexity.

A Mond–Weir type dual model with duality relations analyzed.

Abstract

This paper deals with Pareto solutions of a nonsmooth fractional interval-valued multiobjective optimization. We first introduce four types of Pareto solutions of the considered problem by considering the lower-upper interval order relation and then apply some advanced tools of variational analysis and generalized differentiation to establish necessary optimality conditions for these solutions. Sufficient conditions for Pareto solutions of such a problem are also provided by means of introducing the concepts of (strictly) generalized convex functions defined in terms of the limiting/Mordukhovich subdifferential of locally Lipschitzian functions. Finally, a Mond--Weir type dual model is formulated, and weak, strong and converse-like duality relations are examined.