# Compact representations of structured BFGS matrices

arXiv: https://arxiv.org/abs/2208.00057 · HTML: https://mlsanity.com/paper/2208.00057/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2022.

## Built on by (most cited first, 2 of 2)

- [Useful Compact Representations for Data-Fitting](https://mlsanity.com/paper/2403.12206/) (2024)
- [A Nonmonotone Gradient-Based Algorithm for Symmetric Nonnegative Matrix Factorization and Graph Clustering](https://mlsanity.com/paper/2606.02887/) (2026)

## Abstract (arXiv)

For general large-scale optimization problems compact representations exist in which recursive quasi-Newton update formulas are represented as compact matrix factorizations. For problems in which the objective function contains additional structure, so-called structured quasi-Newton methods exploit available second-derivative information and approximate unavailable second derivatives. This article develops the compact representations of two structured Broyden-Fletcher-Goldfarb-Shanno update formulas. The compact representations enable efficient limited memory and initialization strategies. Two limited memory line search algorithms are described and tested on a collection of problems, including a real world large scale imaging application.