The KKT optimality conditions for optimization problem with interval-valued objective function on Hadamard manifolds. (4th March 2022)

• Record Type: Journal Article
• Authors: Chen, Sheng-lan
• Is Part Of: Optimization. Volume 71:Number 3(2022)
• Page Start: 613
• Page End: 632
• Publication Date: 2022-03-04
• Subjects: gH-directional differentiability -- interval-valued function -- convex and pseudoconvex function -- KKT optimality conditions -- Hadamard manifold; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1810248
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we study the Karush–Kuhn–Tucker optimality conditions in an optimization problem with interval-valued objective function on Hadamard manifolds. The gH -directional differentiability for interval-valued function is defined by using the generalized Hukuhara difference. The concepts of interval-valued convexity and pseudoconvexity are introduced on Hadamard manifolds, and several properties involving such functions are also given. Under these settings, we derive the KKT optimality conditions and give a numerical example to show that the results obtained in this paper are more general than the corresponding conclusions of Wu [The Karush–Kuhn–Tucker optimality conditions in an optimization problem with interval-valued objective function. Eur J Oper Res. 2007;176:46–59] in solving the optimization problem with interval-valued objective function.