# Geometric descent method for convex composite minimization

arXiv: https://arxiv.org/abs/1612.09034 · HTML: https://mlsanity.com/paper/1612.09034/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2016.

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

- [Gradient Descent and the Power Method: Exploiting their connection to find the leftmost eigen-pair and escape saddle points](https://mlsanity.com/paper/2211.00866/) (2022)

## Abstract (arXiv)

In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh to tackle nonsmooth and strongly convex composite problems. We prove that our proposed algorithm, dubbed geometric proximal gradient method (GeoPG), converges with a linear rate (1-1/√kappa) and thus achieves the optimal rate among first-order methods, where kappa is the condition number of the problem. Numerical results on linear regression and logistic regression with elastic net regularization show that GeoPG compares favorably with Nesterov's accelerated proximal gradient method, especially when the problem is ill-conditioned.