Operations Research Transactions ›› 2012, Vol. 16 ›› Issue (1): 115-120.

• Original Articles • Previous Articles     Next Articles

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

 XIA  Shun-You1,2, XU  De-Ping3   

  1. 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

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