The Karush–Kuhn–Tucker conditions for multiple objective fractional interval valued optimization problems

¹ Institute of Fundamental and Frontier Sciences, The University of Electronic Science and Technology of China, Chengdu 610054, PR China
² Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247 667, India

^* Corresponding author: idmath26@gmail.com

Received: 14 January 2019
Accepted: 10 May 2019

Abstract

In this article, we focus on a class of a fractional interval multivalued programming problem. For the solution concept, LU-Pareto optimality and LS-Pareto, optimality are discussed, and some nontrivial concepts are also illustrated with small examples. The ideas of LU-V-invex and LS-V-invex for a fractional interval problem are introduced. Using these invexity suppositions, we establish the Karush–Kuhn–Tucker optimality conditions for the problem assuming the functions involved to be gH-differentiable. Non-trivial examples are discussed throughout the manuscript to make a clear understanding of the results established. Results obtained in this paper unify and extend some previously known results appeared in the literature.