Optimality and duality results for non-smooth vector optimisation problems with K-V-type I functions via local cone approximations
Tadeusz Antczak, Kalpana Shukla · International Journal of Mathematics in Operational Research · 2023
In the paper, local cone approximations are used to introduce new notions of generalised convexity and to prove optimality conditions and duality results for a new class of non-smooth vector optimisation problems with inequality constraints. Namely, several concepts of (generalised) K-V-type I are gathered in a general scheme by means of the concepts of K-directional derivative and the K-subdifferential. Then, optimality conditions and several Mond-Weir duality theorems are established for the considered non-smooth vector optimisation problem. The results established in the paper for aforesaid non-convex non-differentiable vector optimisation problems generalise similar results existing in the literature.