# A homogeneous second-order descent method for nonconvex optimization

arXiv: https://arxiv.org/abs/2211.08212 · HTML: https://mlsanity.com/paper/2211.08212/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2022.

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

- [A Homogenization Approach for Gradient-Dominated Stochastic Optimization](https://mlsanity.com/paper/2308.10630/) (2023)

## Abstract (arXiv)

In this paper, we introduce a Homogeneous Second-Order Descent Method (HSODM) using the homogenized quadratic approximation to the original function. The merit of homogenization is that only the leftmost eigenvector of a gradient-Hessian integrated matrix is computed at each iteration. Therefore, the algorithm is a single-loop method that does not need to switch to other sophisticated algorithms and is easy to implement. We show that HSODM has a global convergence rate of O(ε-3/2) to find an ε-approximate second-order stationary point, and has a local quadratic convergence rate under the standard assumptions. The numerical results demonstrate the advantage of the proposed method over other second-order methods.