For nonsmooth vector optimization, we study conditions for optimality, globality of local solutions, and duality relations, using proposed types of generalized quasiconvexity. Conditions for local minima or maxima of various types to become global minima are proved. Both Karush-Kuhn-Tucker necessary and sufficient conditions are established. Different duality relations are investigated for schemes of the Wolfe and Mond-Weir types.
