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.

摘要

在本文中，我们研究了在 Hadamard 流形上具有区间值目标函数的优化问题中的 Karush-Kuhn-Tucker 最优性条件。GH _区间值函数的方向可微性是通过使用广义 Hukuhara 差分来定义的。在Hadamard流形上引入了区间值凸性和伪凸性的概念，并给出了涉及这些函数的几个性质。在这些设置下，我们推导出了 KKT 最优性条件，并给出了一个数值例子，表明本文得到的结果比 Wu [The Karush-Kuhn-Tucker optimization conditions in an optimization problem with interval-valued目标函数。欧元 J Opera Res。2007;176:46-59] 用区间值目标函数解决优化问题。