上半连续集值优化解在图像逼近意义下的稳定性  

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

作　　者：夏顺友[1,2] 胥德平[3] 

机构地区：[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

出　　处：《运筹学学报》2012年第1期115-120,共6页Operations Research Transactions

基　　金：国家自然科学基金(NO:70661001)

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.In this paper, 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 under the approximate condition of graphic topology. Second, by using the usco researching approach of generic stability, the upper semi-continuity and compact properties of the weakly efficient solutions maps of this optimization problem are proved with the trembles of domain and map. Under the approximate condition of graphic topology, 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.

关 键 词：上(下)半连续 (弱)有效解 本质(弱)有效解 通有连续 

分 类 号：O224[理学—运筹学与控制论]