A Shamanskii-like Levenberg-Marquardt method for nonlinear equations

作者：Fan, Jinyan^*

来源：Computational Optimization and Applications, 2013, 56(1): 63-80.

DOI：10.1007/s10589-013-9549-4

• Nonlinear equations
• Levenberg-Marquardt method
• Local error bound condition

In this paper, we propose a Shamanskii-like Levenberg-Marquardt method for nonlinear equations. At every iteration, not only a LM step but also m-1 approximate LM steps are computed, where m is a positive integer. Under the local error bound condition which is weaker than nonsingularity, we show the Shamanskii-like LM method converges with Q-order m 1. The trust region technique is also introduced to guarantee the global convergence of the method. Since the Jacobian evaluation and matrix factorization are done after every m computations of the step, the overall cost of the Shamanskii-like LM method is usually much less than that of the general LM method (the m=1 case).

• 出版日期2013-9
• 单位上海交通大学