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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.
Acknowledgments
The author is grateful to the editor and the referees for their valuable comments and suggestions. This work was supported by Chongqing Research Program of Basic Research and Frontier Technology (No. cstc2018jcyjAX0605), Scientific and Technological Research Program of Chongqing Municipal Education Commission (No. KJ1600433), and Foundation of Chongqing University of Posts and Telecommunications for the Scholars with Doctorate.
Disclosure statement
No potential conflict of interest was reported by the author(s).