上半连续集值优化解在图像逼近意义下的稳定性

运筹学学报 ›› 2012, Vol. 16 ›› Issue (1): 115-120.

上半连续集值优化解在图像逼近意义下的稳定性

夏顺友^1,2, 胥德平³

1. 贵州大学计算机科学与信息学院, 贵阳, 550025; 2. 贵州师范学院数学与计算机科学学院,贵阳, 550018; 3. 成都理工大学数学地质四川省重点实验室, 成都, 610059

收稿日期:2011-06-10 修回日期:2012-02-24 出版日期:2012-03-15 发布日期:2012-03-15
通讯作者: 夏顺友 E-mail:xiashunyou@126.com
基金资助:
国家自然科学基金

The Stability of the Solutions of Optimization Problem for Set-Valued Maps With Upper Semi-continuity Under Graphic Approximate

XIA Shun-You^1,2, XU De-Ping³

1. College of Computer Science and Information, Guizhou University, Guiyang 550025, China; 2. Department of Mathematics and Computer, Guizhou Normal College, Guiyang 550018, China; 3. Key Laboratory of Geomathematics of Sichuan Province, Chengdu University of Technology, Chengdu 610059, China

Received:2011-06-10 Revised:2012-02-24 Online:2012-03-15 Published:2012-03-15
Contact: Shun-You XIA E-mail:xiashunyou@126.com

摘要/Abstract

摘要： 给出上半连续集值映射优化问题在图像拓扑逼近意义下的本质弱有效解和本质有效解的概念.利用通有稳定性研究的usco方法, 证明了上半连续集值映射优化问题.在图像拓扑逼近意义下,弱有效解映射在定义域和映射同时扰动下是紧值上半连续的,从而是通有下半连续的,即在Baire纲意义下, 绝大多数上半连续集值映射优化问题, 在图像逼近意义下其弱有效解是稳定的,或者说是本质的. 证明了上半连续集值映射优化问题在图像逼近意义下有效解映射上半连续的一个充要条件,也即是有效解通有稳定的一个重要条件.

关键词: 上(下)半连续, (弱)有效解, 本质(弱)有效解, 通有连续

Abstract: In this paper, under the approximate condition of graphic topology, we first introduce the essential efficient solutions and the weakly essential efficient solutions of the optimization problem for upper semi-continuity maps with set-value. Second, by using the usco researching approach of generic stability, with the trembles of domain and map, the upper semi-continuity and compact properties of the weakly efficient solutions maps of this optimization problem are proved, under the approximate condition of graphic topology, and then it is generic lower semi-continuous, that is to say, in the sense of Baire Category, weakly efficient solutions maps of “most” this optimization problems are generic stability(i.e. essential) under the approximate condition of graphic topology. Last, we prove a necessary and sufficient condition of upper semi-continuity of the efficient solutions maps of this optimization problem.

Key words: upper(lower)-semi-continuity, (weakly) efficient solution, essential (weakly) efficient solution, generic continuity

夏顺友, 胥德平. 上半连续集值优化解在图像逼近意义下的稳定性[J]. 运筹学学报, 2012, 16(1): 115-120.

XIA Shun-You, XU De-Ping. The Stability of the Solutions of Optimization Problem for Set-Valued Maps With Upper Semi-continuity Under Graphic Approximate[J]. Operations Research Transactions, 2012, 16(1): 115-120.