generalized (phi, rho)-convexity in nonsmooth vector optimization over cones

In this paper, new classes of cone-generalized (Phi,Rho)-convex functions are introduced for a nonsmooth vector optimization problem over cones, which subsume several known studied classes. Using these generalized functions,  various sufficient Karush-Kuhn-Tucker (KKT) type  nonsmooth optimality conditions are established wherein Clarke's generalized gradient is used. Further, we prove duality results for both Wolfe and Mond-Weir type duals under various types of cone-generalized (Phi,Rho)-convexity assumptions.Phi,Rho