Algebraic rules for computing the regularization parameter of the Levenberg-Marquardt method

作者：Karas Elizabeth W^*; Santos Sandra A; Svaiter Benar F

来源：Computational Optimization and Applications, 2016, 65(3): 723-751.

DOI：10.1007/s10589-016-9845-x

• Nonlinear least-squares problems
• Levenberg-Marquardt method
• Regularization
• Global convergence
• Local convergence
• Computational results

This paper presents a class of Levenberg-Marquardt methods for solving the nonlinear least-squares problem. Explicit algebraic rules for computing the regularization parameter are devised. In addition, convergence properties of this class of methods are analyzed. We prove that all accumulation points of the generated sequence are stationary. Moreover, q-quadratic convergence for the zero-residual problem is obtained under an error bound condition. Illustrative numerical experiments with encouraging results are presented.

• 出版日期2016-12