解非线性单调方程组的投影自调比对称秩1拟牛顿法

运筹学学报 ›› 2010, Vol. 14 ›› Issue (3): 64-72.

解非线性单调方程组的投影自调比对称秩1拟牛顿法

刘浩, 钱小燕, 倪勤

出版日期:2010-09-15 发布日期:2010-09-15

rojected Self-Scaling Symmetric Rank One Quasi－Newton Methods for Nonlinear Monotone Equations

LIU Hao, QIAN Xiao-Yan, NI Qin

Online:2010-09-15 Published:2010-09-15

摘要/Abstract

摘要： 本文给出了求解非线性单调方程组的两个自调比对称秩1牛顿法，即投影SSR1法和投影有限储存SSR1法.这两个算法将自调比对称秩1校正参数进行了一个简单的修改并采用了保守策略. 在非线性单调函数满足李普希茨连续的条件下，证明了算法的全局收敛性，并与相同类型的BFGS法进行了初步的数值比较试验，试验结果表明自调比对称秩1类投影算法求解非线性单调方程组与相同类型的BFGS数值结果相当.

关键词: font-family: 宋体, mso-bidi-font-family: 宋体, mso-font-kerning: 1.0pt, mso-ansi-language: EN-US, mso-fareast-language: ZH-CN, mso-bidi-language: AR-SA"> , 运筹学, 自调比对称秩1校正, 有限储存, 非线性单调方程组, 投影方法

Abstract: In this paper, two self-scaling symmetric rank one algorithms with projection are proposed for solving nonlinear monotone equations. In the two algorithms, a simple rule in choosing parameters in symmetric rank one is modified and a cautious update rule is used. Under the condition that the nonlinear monotone function is Lipschitz continuous, the global convergence of these two algorithms is proved. Compared with the same type BFGS algorithms, some preliminary numerical experiments are also done. The results indicate that the numerical performance of SSR1 class algorithms may be competitive with that of the counterparts.

刘浩, 钱小燕, 倪勤. 解非线性单调方程组的投影自调比对称秩1拟牛顿法[J]. 运筹学学报, 2010, 14(3): 64-72.

LIU Hao, QIAN Xiao-Yan, NI Qin. rojected Self-Scaling Symmetric Rank One Quasi－Newton Methods for Nonlinear Monotone Equations[J]. Operations Research Transactions, 2010, 14(3): 64-72.