有界约束非线性系统的结合Lanczos分解技术不精确Newton法  

Inexact Newton Method via Lanczos Decomposed Technique for Solving Box-Constrained Nonlinear Systems

作　　者：张勇[1] 朱德通[2] 

机构地区：[1]上海师范大学数理学院,上海200234 [2]上海师范大学商学院,上海200234

出　　处：《应用数学和力学》2010年第12期1503-1512,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10871130);教育部博士点基金资助项目(20093127110005);上海市重点学科资助项目(T0401)

摘　　要：提出了结合Lanczos分解技术不精确Newton法求解有界变量约束非线性系统.通过Lanc-zos分解技术解一个仿射二次模型获得迭代方向.利用内点回代线搜索技术,沿着这个方向得到一个可接受的步长.在合理的假设条件下,证明了算法的整体收敛性与局部超线性收敛速率.此外,数值结果表明了算法的有效性.An inexact Newton method via Lanczos decomposed technique was proposed for solving the box-constrained nonlinear systems.The iterative direction was obtained by solving an affine scaling quadratic model with Lanczos decomposed technique.By using the interior backtracking line search technique,the acceptable trial step length along this direction will be found.The global convergence and fast local convergence rate of the proposed algorithm were established under some reasonable conditions.Furthermore,the results of the numerical experiments are reported to show the effectiveness of the proposed algorithm.

关 键 词：非线性系统 LANCZOS方法 不精确NEWTON法 非单调技术 

分 类 号：O221.2[理学—运筹学与控制论]