Optimality and duality in nonsmooth vector optimization with non-convex feasible set

Abstract

For a convex programming problem, the Karush–Kuhn–Tucker (KKT) conditions are necessary and sufficient for optimality under suitable constraint qualification. Recently, Suneja et al. [Am. J. Oper. Res. 6 (2013) 536–541] proved KKT optimality conditions for a differentiable vector optimization problem over cones in which they replaced the cone-convexity of constraint function by convexity of feasible set and assumed the objective function to be cone-pseudoconvex. In this paper, we have considered a nonsmooth vector optimization problem over cones and proved KKT type sufficient optimality conditions by replacing convexity of feasible set with the weaker condition considered by Ho [Optim. Lett. 11 (2017) 41–46] and assuming the objective function to be generalized nonsmooth cone-pseudoconvex. Also, a Mond–Weir type dual is formulated and various duality results are established in the modified setting.