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

Comparison Principle For Quasilinear Parabolic Inclusions with Clarke’s Gradient

We prove existence and comparison results for quasilinear parabolic inclusions with Clarke’s generalized gradient via appropriately defined sub-supersolution only assuming a local L