The KKT optimality conditions for optimization problem with interval-valued objective function on Hadamard manifolds

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.