The modified Levenberg–Marquardt method with nonmonotone technique
Abstract
In this paper, we propose a modified Levenberg–Marquardt (LM) method with a nonmonotone technique for solving nonlinear equations. Under the $ \mathrm{H\ddot{o}lderian} $ continuity and the $ \mathrm{H\ddot{o}lderian} $ local error bounds conditions, which are weaker than the local error bounds and the Lipschitz continuity, the global convergence and local convergence of the algorithm are proved. Numerical experiments also show that the algorithm is effective.
Fields of Study & Subjects
Advanced Optimization Algorithms Research
Iterative Methods for Nonlinear Equations
Matrix Theory and Algorithms
Publication details
- Journal / source
- AIMS Mathematics
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 11
- Issue
- 1
- Pages
- 2527–2546
- Publication date
- 1 January 2026