A Levenberg-Marquardt algorithm with correction for singular system of nonlinear equations

作者：Fan, Jinyan^*; Zeng, Jinlong

来源：Applied Mathematics and Computation, 2013, 219(17): 9438-9446.

DOI：10.1016/j.amc.2013.03.026

• Singular nonlinear equations
• Levenberg-Marquardt method
• Correction technique
• Local error bound
• Trust region method

In this paper we propose anew LM algorithm for the singular system of nonlinear equations F(x) = 0, where F(x) : R-n -> R-n is continuously differentiable and F'(x) is Lipschitz continuous. At every iteration, not only a LM step but also a correction step are computed. The LM parameter is taken as mu(k)parallel to F-k parallel to(delta), where delta is an element of (0, 2] and mu(k) is updated by the trust region technique. Under the local error bound condition which is weaker than nonsingularity, we prove the convergence rate of the algorithm is min {2, 1 2 delta}. Numerical results show that the new LM algorithm performs very well.

• 出版日期2013-5-1
• 单位上海交通大学