Title: Optimality and duality results for non-smooth vector optimisation problems with K-V-type I functions via local cone approximations

Authors: Tadeusz Antczak; Kalpana Shukla

Addresses: Faculty of Mathematics and Computer Science, University of Lodz, Poland ' Department of Mathematics, Zakir Husain Delhi College (Evening), University of Delhi, New Delhi, India

Abstract: 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.

Keywords: non-smooth multi-objective programming; local cone approximations; K-directional derivative; K-subdifferential; K-V-type I function.

DOI: 10.1504/IJMOR.2024.140071

International Journal of Mathematics in Operational Research, 2024 Vol.28 No.3, pp.374 - 395

Received: 28 Feb 2023
Accepted: 28 Feb 2023
Published online: 19 Jul 2024 *

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