# Parameter-Free Accelerated Quasi-Newton Method for Nonconvex Optimization

arXiv: https://arxiv.org/abs/2512.09439 · HTML: https://mlsanity.com/paper/2512.09439/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2025.

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

- [A Parameter-Free First-Order Algorithm for Non-Convex Optimization with tildemkern1mu O(ε-5/3) Global Rate](https://mlsanity.com/paper/2605.02127/) (2026)

## Abstract (arXiv)

We propose a quasi-Newton-type method for nonconvex optimization with Lipschitz continuous gradients and Hessians. The algorithm finds an varepsilon-stationary point within O(d1/4 varepsilon-13/8) function and gradient evaluations, where d is the problem dimension. Our method is parameter-free in the sense that it requires no prior knowledge of problem-dependent parameters such as Lipschitz constants or the optimal value. Moreover, it does not need the target accuracy varepsilon or the total number of iterations to be specified in advance. The result is achieved by combining several key ideas: momentum-based acceleration, quartic regularization for subproblems, and a scaled variant of the Powell-symmetric-Broyden (PSB) update.