# Efficient Regularized Proximal Quasi-Newton Methods for Large-Scale Nonconvex Composite Optimization Problems

arXiv: https://arxiv.org/abs/2210.07644 · HTML: https://mlsanity.com/paper/2210.07644/

## Key facts

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

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

- [A Proximal Modified Quasi-Newton Method for Nonsmooth Regularized Optimization](https://mlsanity.com/paper/2409.19428/) (2024)

## Abstract (arXiv)

Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their generalizations like proximal Newton and quasi-Newton methods. In this paper, we propose a regularized proximal quasi-Newton method whose main features are: (a) the method is globally convergent to stationary points, (b) the globalization is controlled by a regularization parameter, no line search is required, (c) the method can be implemented very efficiently based on a simple observation which combines recent ideas for the computation of quasi-Newton proximity operators and compact representations of limited-memory quasi-Newton updates. Numerical examples for the solution of convex and nonconvex composite optimization problems indicate that the method outperforms several existing methods.