On approximate quasi Pareto solutions in nonsmooth semi-infinite interval-valued vector optimization problems

TL;DR

This paper introduces new types of approximate solutions for nonsmooth semi-infinite interval-valued vector optimization problems, establishes optimality conditions, and explores duality relations using advanced variational analysis tools.

Contribution

It defines four types of approximate quasi Pareto solutions and provides necessary and sufficient optimality conditions using generalized differentiation.

Findings

Established necessary optimality conditions for approximate solutions.

Provided sufficient conditions using generalized convexity concepts.

Formulated a dual model with duality relations in the approximate setting.

Abstract

This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multiple interval-valued objective functions. We first introduce four types of approximate quasi 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 approximate solutions. Sufficient conditions for approximate quasi Pareto solutions of such a problem are also provided by means of introducing the concepts of approximate (strictly) pseudo-quasi generalized convex functions defined in terms of the limiting subdifferential of locally Lipschitz functions. Finally, a Mond--Weir type dual model in approximate form is formulated, and weak, strong and converse-like duality relations are proposed.