Title: Local cone approximations in non-smooth K-univex multi-objective programming problems

Authors: Tadeusz Antczak; Kalpana Shukla

Addresses: Faculty of Mathematics and Computer Science, University of Lodz, Poland ' Department of Mathematics, Manav Rachna University, Faridabad, India

Abstract: In this paper, we have established some results for a new class of non-smooth multi-objective problems with both inequality and equality constraints are considered. Several definitions of non-smooth (generalised) K-univex functions are gathered in a general scheme by means of the concepts of K-directional derivative and the K-subdifferential. Then, local cone approximations are used to obtain optimality and Mond-Weir duality results for aforesaid non-smooth multi-objective problems with (generalised) K-univex functions. The results established in this paper extend similar results existing in the literature to new classes of non-convex non-differentiable multi-objective programming problems. Some examples are also given for our findings.

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

DOI: 10.1504/IJMOR.2023.135550

International Journal of Mathematics in Operational Research, 2023 Vol.26 No.4, pp.425 - 448

Received: 31 Aug 2022
Accepted: 02 Sep 2022
Published online: 18 Dec 2023 *

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