# A proximal Newton framework for composite minimization: Graph learning without Cholesky decompositions and matrix inversions

arXiv: https://arxiv.org/abs/1301.1459 · HTML: https://mlsanity.com/paper/1301.1459/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2013.

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

- [Fast Projected Newton-like Method for Precision Matrix Estimation under Total Positivity](https://mlsanity.com/paper/2112.01939/) (2021)

## Abstract (arXiv)

We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that features a local quadratic convergence rate. As a specific instance of our framework, we consider the sparse inverse covariance matrix estimation in graph learning problems. Via a careful dual formulation and a novel analytic step-size selection procedure, our approach for graph learning avoids Cholesky decompositions and matrix inversions in its iteration making it attractive for parallel and distributed implementations.