# Convergence and Complexity Analysis of a Levenberg-Marquardt Algorithm for Inverse Problems

arXiv: https://arxiv.org/abs/2004.03005 · HTML: https://mlsanity.com/paper/2004.03005/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2020.

## Built on by (most cited first, 4 of 4)

- [FedNew: A Communication-Efficient and Privacy-Preserving Newton-Type Method for Federated Learning](https://mlsanity.com/paper/2206.08829/) (2022)
- [Regularized Newton Method with Global O(1/k2) Convergence](https://mlsanity.com/paper/2112.02089/) (2021)
- [Dual Gauss-Newton Directions for Deep Learning](https://mlsanity.com/paper/2308.08886/) (2023)
- [Neural Network-Based Parameter Estimation for Non-Autonomous Differential Equations with Discontinuous Signals](https://mlsanity.com/paper/2507.06267/) (2025)

## Abstract (arXiv)

The Levenberg-Marquardt algorithm is one of the most popular algorithms for finding the solution of nonlinear least squares problems. Across different modified variations of the basic procedure, the algorithm enjoys global convergence, a competitive worst case iteration complexity rate, and a guaranteed rate of local convergence for both zero and nonzero small residual problems, under suitable assumptions. We introduce a novel Levenberg-Marquardt method that matches, simultaneously, the state of the art in all of these convergence properties with a single seamless algorithm. Numerical experiments confirm the theoretical behavior of our proposed algorithm.