A corrected Levenberg-Marquardt algorithm with a nonmonotone line search for the system of nonlinear equations

作者：He, Yedan; Ma, Changfeng^*; Fan, Bin

来源：Applied Mathematics and Computation, 2015, 260: 159-169.

DOI：10.1016/j.amc.2015.03.076

• The system of nonlinear equations
• L-M method
• Corrected step
• Nonmonotone line search
• Global and cubic convergence

In this paper, we propose a corrected Levenberg-Marquardt method for the system of non-linear equations, in which not only an L-M step and a corrected step are computed at every iteration but also a nonmonotone line search to find a new iteration point will be performed if a trial step is not accepted. To ensure the global convergence of the new method, a new nonmonotone line search technique is introduced for the merit function. The cubic convergence of the new method is proved under the local error bound condition which is weaker than nonsingularity. Some numerical results are reported, which shows that the algorithm is quite effective.

• 出版日期2015-6-1
• 单位福建师范大学