Second Order Duality in Multiobjective Programming Involving Generalized Type I Functions

Abstract

Recently Hachimi and Aghezzaf introduced the notion of (F, α, ρ, d)-type I functions, a new class of functions that unifies several concepts of generalized type I functions. In this paper, we extend the notion of (F, α, ρ, d)-type I functions to second order and establish several mixed duality results under second order generalized (F, α, ρ, p, d)-type I functions. Our results generalize the duality results recently given by Aghezzaf [Aghezzaf, B. (2003). Second order mixed type duality in multiobjective programming problems. J. Math. Anal. Appl. 285:97–106] and Hachimi and Aghezzaf [Hachimi, M., Aghezzaf, B. (2004). Sufficiency and duality in differentiable multiobjective programming involving generalized type I functions. J. Math. Anal. Appl. 296:382–392].