In this paper, we introduce a new class of higher-order cone-convex, $$(K_1, K_2)$$ (K1,K2) -pseudoconvex and quasiconvex functions which encapsulates several already known functions. Higher-order sufficient optimality conditions have been established for a vector optimization problem over cones by using these functions, under weaker conditions on multipliers as compared to other papers in this domain. Wolfe type and Mond–Weir type higher-order duals are formulated and corresponding duality results are established. A number of previously studied problems appear as special cases of our primal-dual models. In case of nonlinear programming problem, our higher-order duals reduce to the corresponding higher-order duals given by Mangasarian (J Math Anal Appl 51:607–620, 1975) and Mond and Zhang (Generalized convexity, generalized monotonicity: recent results. Kluwer, Dordrecht, pp 357–372, 1998).