New Concepts of Generalized Convexity in Multiobjective Subset Programming

In this paper, a new class of nonconvex differentiable multiobjective programming problems involving n-set functions with both inequality and equality constraints is considered.Then, under V-r-convexity and/or generalized V-r-convexity hypotheses, several sufficient optimality conditions, saddle point criteria and various mixed duality theorems are proved for such not necessarily convex vector optimization problems involving n-set functions.