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In this paper, a nondifferentiable multiobjective programming problem is considered where every component of objective and constraint functions contain a term involving the support function of a compact convex set. A new class of higher order ( F, α, ρ, d)-type I function is introduced. Necessary optimality conditions and the duality theorems for Wolfe and unified higher order dual problems are established. Several known results can be deduced as special cases. [ABSTRACT FROM AUTHOR]

In this paper, a new class of second-order (F, α, ρ, d)-V-type I functions is introduced that generalizes the notion of (F, α, ρ, θ)-V-convex functions introduced by Zalmai (Computers Math. Appl. 2002; 43:1489-1520) and (F, α, ρ, p, d)-type I functions defined by Hachimi and Aghezzaf (Numer. Funct. Anal. Optim. 2004; 25:725-736). Based on these functions, weak, strong, and strict converse duality theorems are derived for Wolfe and Mond-Weir type multiobjective dual programs in order to relate the efficient and weak efficient solutions of primal and dual problems. [ABSTRACT FROM AUTHOR]