Sufficiency and Duality in Multiobjective Variational Problems with Generalized Type I Functions

摘要

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. Here, we extend the concepts of (F, α, ρ, d)-type I and generalized (F, α, ρ, d)-type I functions to the continuous case and we use these concepts to establish various sufficient optimality conditions and mixed duality results for multiobjective variational problems. Our results apparently generalize a fairly large number of sufficient optimality conditions and duality results previously obtained for multiobjective variational problems.