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Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (12): 1593-1602.doi: https://doi.org/10.1007/s10483-010-1387-x

• Articles • 上一篇    

Inexact Newton method via Lanczos decomposed technique for solving box-constrained nonlinear systems

张勇1 朱德通2   

  1. 1. Mathematics and Science College, Shanghai Normal University, Shanghai 200234, P. R. China;
    2. Business College, Shanghai Normal University, Shanghai 200234, P. R. China
  • 收稿日期:2010-03-14 修回日期:2010-11-01 出版日期:2010-12-01 发布日期:2010-12-01

Inexact Newton method via Lanczos decomposed technique for solving box-constrained nonlinear systems

ZHANG Yong1, ZHU De-Tong2   

  1. 1. Mathematics and Science College, Shanghai Normal University, Shanghai 200234, P. R. China;
    2. Business College, Shanghai Normal University, Shanghai 200234, P. R. China
  • Received:2010-03-14 Revised:2010-11-01 Online:2010-12-01 Published:2010-12-01

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被引次数

2

摘要： This paper proposes an inexact Newton method via the Lanczos decomposed technique for solving the box-constrained nonlinear systems. An iterative direction is obtained by solving an affine scaling quadratic model with the Lanczos decomposed technique. By using the interior backtracking line search technique, an acceptable trial step length is found along this direction. The global convergence and the fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the results of the numerical experiments show the effectiveness of the proposed algorithm.

Abstract: This paper proposes an inexact Newton method via the Lanczos decomposed technique for solving the box-constrained nonlinear systems. An iterative direction is obtained by solving an affine scaling quadratic model with the Lanczos decomposed technique. By using the interior backtracking line search technique, an acceptable trial step length is found along this direction. The global convergence and the fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the results of the numerical experiments show the effectiveness of the proposed algorithm.

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