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...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 pro- posed algorithm.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10871130)the Ph. D.Programs Foundation of Ministry of Education of China (No. 20093127110005)the Shanghai Leading Academic Discipline Project (No. T0401)
文摘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 pro- posed algorithm.
