求解极大相关问题的对偶方法  

A Dual Method for the Maximal Correlation Problem

作　　者：李美然[1] 刘新国[1] 

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2015年第8期128-132,共5页Periodical of Ocean University of China

基　　金：国家自然科学基金项目(11371333)资助

摘　　要：多组变量间的极大相关问题(MCP)有重要统计应用。目前已有的求解MCP的算法都不能保证获得MCP的全局解。本文通过求解MCP的对偶问题,给出了一种改进的Lagrange对偶方法。最后,数值实验结果说明了新方法能提高收敛到全局解的可能性。The maximal correlation problem aiming at assessing the relationship between sets of variables plays a very important role in many areas of statistical application.Currently,several algorithms for the global maximizer of the MCP have been proposed,but they can not guarantee convergence to a global solution.In the present paper,by solving the dual problem of the MCP,a modified Lagrange dual method is proposed.Numerical experiments demonstrate the new algorithm can increase the probability of finding aglobal maximizer.

关 键 词：极大相关问题 多元特征值问题 LAGRANGE对偶 强对偶 全局解 收敛性 

分 类 号：O212.4[理学—概率论与数理统计]