Convergence Properties of a Self-adaptive Levenberg-Marquardt Algorithm Under Local Error Bound Condition

Authors:
Jinyan Fan;Jianyu Pan
Affiliations:
Aff1 Aff2;Department of Mathematics, East China Normal University, Shanghai, P.R. China 200062
Venue:
Computational Optimization and Applications
Year:
2006

Citing 2
Cited 1

Testing Unconstrained Optimization Software

ACM Transactions on Mathematical Software (TOMS)
On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption

Computing

On the local convergence of a derivative-free algorithm for least-squares minimization

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We propose a new self-adaptive Levenberg-Marquardt algorithm for the system of nonlinear equations F(x) = 0. The Levenberg-Marquardt parameter is chosen as the product of 驴Fk驴驴 with 驴 being a positive constant, and some function of the ratio between the actual reduction and predicted reduction of the merit function. Under the local error bound condition which is weaker than the nonsingularity, we show that the Levenberg-Marquardt method converges superlinearly to the solution for 驴驴 (0, 1), while quadratically for 驴驴 [1, 2]. Numerical results show that the new algorithm performs very well for the nonlinear equations with high rank deficiency.