# Complexity of the Regularized Newton Method

arXiv: https://arxiv.org/abs/1706.08483 · HTML: https://mlsanity.com/paper/1706.08483/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2017.

## Built on by (most cited first, 1 of 1)

- [Simple Stepsize for Quasi-Newton Methods with Global Convergence Guarantees](https://mlsanity.com/paper/2508.19712/) (2025)

## Abstract (arXiv)

Newton's method for finding an unconstrained minimizer for strictly convex functions, generally speaking, does not converge from any starting point. We introduce and study the damped regularized Newton's method (DRNM). It converges globally for any strictly convex function, which has a minimizer in Rn. Locally DRNM converges with a quadratic rate. We characterize the neighborhood of the minimizer, where the quadratic rate occurs. Based on it we estimate the number of DRNM's steps required for finding an varepsilon- approximation for the minimizer.