向量优化问题真有效点的锥刻画  

Cone characterizations of proper efficient points in vector optimization

作　　者：陈林[1] 赵洁[1] 姜艮[1] 

机构地区：[1]重庆师范大学数学学院,重庆400047

出　　处：《沈阳师范大学学报（自然科学版）》2011年第4期486-489,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：重庆市自然科学基金资助项目(CSTC2010BB2090);重庆市教委研究项目(KJ100608)

摘　　要：在向量优化问题中最佳目标值的存在性与求解始终是研究的核心问题,其实质是在目标函数的可行域中寻找使目标值在一定意义下的最佳点,而有效点、弱有效点和真有效点正是表征了点在集合中的某种最佳性。在一般向量优化问题的目标空间中研究了2种真有效点-Henig真有效点和Hurwicz真有效点的锥刻画。主要利用集合在某点的相依锥、法向锥和可行方向锥对向量优化问题的真有效点的特征进行了刻画。首先,利用切向锥与负序锥的位置关系式来给出成为Henig真有效点和Hurwicz真有效点的充分必要条件。然后,利用这些结果,得到了这2种真有效点概念等价的一个充分条件。最后,在对偶空间中,用法向锥与锥间的位置关系式来给出是成为凸子集中Henig真有效点的充分必要条件。The existence of the optima and how to obtain it are always the keys in vector optimization problems,and the essence of the probtem is to find the optima under some conditions in the domain of the objective function,while efficient,weak efficient and proper efficient points are exactly characterizing the optimization of the points which belong to the set.In this paper we studied cone characterizations in two types of proper efficient points—Henig proper efficient points and Hurwicz proper efficient points in the objective space of general vector optimization problem.These were mainly presented with the help of contigent cones, normal cones and feasible directions cones of a set at a point.Using these results,we obtain the sufficient condition that these concepts of properly efficient points are equivalent.Then we give a necessary and sufficient condition that is the Henig proper efficient point of described by the formulation between the normal cone and the cone in the topological dual space.

关 键 词：向量优化问题 Henig真有效点 Hurwicz真有效点 锥刻画 

分 类 号：O221.2[理学—运筹学与控制论]