Optimality and duality for approximate solutions of multiobjective optimization problems involving intersection of closed sets

In this paper, we investigate optimality conditions for epsilon-quasi efficient solutions of nonsmooth/nonconvex multiobjective optimization problems involving intersection of closed sets in terms of the Mordukhovich subdifferentials. Furthermore, we also obtain types of Wolfe and Mond-Weir dual problem for the primal problem under suitable assumptions on the generalized convexity via the Mordukhovich subdifferentials. Besides, we introduce epsilon-quasi saddle point theorems with respect to nonsmooth/nonconvex multiobjective optimization problems involving intersection of closed sets. Finally, we provide an application to a nonsmooth/nonconvex fractional multiobjective optimization problem involving intersection of closed sets. The obtained results improve or include some recent known ones. Several illustrative examples are also provided.