# Practical Inexact Proximal Quasi-Newton Method with Global Complexity Analysis

arXiv: https://arxiv.org/abs/1311.6547 · HTML: https://mlsanity.com/paper/1311.6547/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2013.

## Built on by (most cited first, 4 of 4)

- [Accelerating nuclear-norm regularized low-rank matrix optimization through Burer-Monteiro decomposition](https://mlsanity.com/paper/2204.14067/) (2022)
- [Accelerated Quasi-Newton Proximal Extragradient: Faster Rate for Smooth Convex Optimization](https://mlsanity.com/paper/2306.02212/) (2023)
- [Augmented Newton Method for Optimization: Global Linear Rate and Momentum Interpretation](https://mlsanity.com/paper/2205.11033/) (2022)
- [Simple Stepsize for Quasi-Newton Methods with Global Convergence Guarantees](https://mlsanity.com/paper/2508.19712/) (2025)

## Abstract (arXiv)

Recently several methods were proposed for sparse optimization which make careful use of second-order information [10, 28, 16, 3] to improve local convergence rates. These methods construct a composite quadratic approximation using Hessian information, optimize this approximation using a first-order method, such as coordinate descent and employ a line search to ensure sufficient descent. Here we propose a general framework, which includes slightly modified versions of existing algorithms and also a new algorithm, which uses limited memory BFGS Hessian approximations, and provide a novel global convergence rate analysis, which covers methods that solve subproblems via coordinate descent.