Sufficiency and Duality for Nonsmooth Multiobjective Programming Problems Involving Generalized (Φ, ρ)-V-Type I Functions

Abstract

In this paper, a class of nonsmooth multiobjective programming problems is considered. We introduce the new concepts of (Φ, ρ)-V-type I, (pseudo, quasi) (Φ, ρ)-V-type I and (quasi, pseudo) (Φ, ρ)-V-type I functions, in which the involved functions are locally Lipschitz. Based upon these generalized (Φ, ρ)-V-type I functions, the sufficient optimality conditions for weak efficiency, efficiency and proper efficiency are derived. Mond-Weir duality results are also established under the aforesaid functions.