Higher-order generalized convexity and duality in nondifferentiable multiobjective mathematical programming

In this paper, a class of generalized convexity is introduced and a unified higher-order dual model for nondifferentiable multiobjective programs is described, where every component of the objective function contains a term involving the support function of a compact convex set. Weak duality theorems are established under generalized convexity conditions. The well-known case of the support function in the form of square root of a positive semidefinite quadratic form and other special cases can be readily derived from our results.