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

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.