可达到和可逼近总极小点的存在性和最优性

运筹学学报 ›› 2012, Vol. 16 ›› Issue (2): 32-40.

可达到和可逼近总极小点的存在性和最优性

姚奕荣¹, 安柳¹, 陈熙¹, 郑权²

1. 上海大学数学系, 上海，200444；
2. 美国哥伦布州立大学数学系，哥伦布，GA 31907

收稿日期:2011-03-01 修回日期:2012-03-29 出版日期:2012-06-15 发布日期:2012-06-15
通讯作者: 姚奕荣 E-mail:yryao@staff.shu.edu.cn
基金资助:
国家自然科学基金资助项目;上海市重点学科项目建设

Existence and Optimality of Accessible and Approximatable Minimizers for Global Optimization with Deviation Integral

Yao Yirong¹, AN Liu¹, CHEN Xi¹, ZHENG Quan²

1. Department of Mathematics, Shanghai University, Shanghai 200444, China; 2. Department of Mathematics, Columbus State University, Columbus, GA 31907

Received:2011-03-01 Revised:2012-03-29 Online:2012-06-15 Published:2012-06-15

摘要/Abstract

摘要： 针对积分总极值，讨论并拓展了丰满集和丰满函数的概念，研究了拟上丰满和伪上丰满函数的总极值问题. 在总极值的变差积分最优性条件下，证明了拟上丰满函数的可达到极小点和伪上丰满函数的可逼近极小点的存在性.

关键词: 总极值问题, 丰满极小点, 拟上半丰满, 变差积分

Abstract: The concepts of robustness of sets and functions are proposed in view of the theory of integral global minimization. These concepts are generalized, and global minimization of quasi and pseudo upper robust function is investigated in this paper. With the deviation integral optimality condition of global minimum, the existence of accessible minimizer of quasi upper functions and approximatable minimizer of pseudo upper robust function is examined..

Key words: global optimization, robust minimizer, quasi upper robust, deviation integral

姚奕荣, 安柳, 陈熙, 郑权. 可达到和可逼近总极小点的存在性和最优性[J]. 运筹学学报, 2012, 16(2): 32-40.

Yao-Yi-Rong, AN Liu, CHEN Xi, ZHENG Quan. Existence and Optimality of Accessible and Approximatable Minimizers for Global Optimization with Deviation Integral[J]. Operations Research Transactions, 2012, 16(2): 32-40.