求解半光滑方程组的非精确Newton法  

Inexact Newton Methods for Solving Systemsof Semismooth Equations

作　　者：张鑫[1] 路永洁[2] 

机构地区：[1]大连理工大学应用数学系,辽宁大连116024 [2]抚顺石油学院数理部,辽宁抚顺113001

出　　处：《石油化工高等学校学报》2002年第1期78-80,共3页Journal of Petrochemical Universities

摘　　要：1977年Mifflin提出了半光滑函数这一概念。Qi与Sun将它推广到映射的情形。映射F :Rn→Rm 在x点被称为是半光滑的 ,若F在x附近是Lipschitz连续的 ,且对任意的h∈Rn,极限limV∈F(x +th′)h′→h ,t↓ 0{Vh′]存在。半光滑函数 (映射 )类覆盖许多的重要函数 ,如光滑函数、凸函数、分片光滑函数 ,半光滑函数的复合函数等。给出半光滑方程组的非精确Newton算法 ,证明了产生的序列是局部收敛的 ,且在一定条件下收敛速度是超线性的 。In 1977, Mifflin introduced the idea of semismooth function. Qi and Sun put it into mapping. Mapping F:R n→R m was called semismooth in x if F was Lipschitz continuous and lim V∈ ( x+th′)h′→h,t↓ 0{ Vh ′} was exist for all h∈R n semismooth functions (mappings) cover many important function, such as smooth function, convex function, semismooth function so on. In this paper, inexact Netwon methods for solving systems of semismooth equations are presented. We prove that such methods are locally corvergent and the rate of convergence is superlinear under certain conditions. Finally, we characterize the order of conrergence in terms of the rate of convergence of the relative residuals.

关 键 词：非精确Newton法 半光滑映射 超线性收敛 半光滑方程组 求解 

分 类 号：O241.7[理学—计算数学]