# On the global convergence of randomized coordinate gradient descent for non-convex optimization

arXiv: https://arxiv.org/abs/2101.01323 · HTML: https://mlsanity.com/paper/2101.01323/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2021.

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

- [Cyclic Block Coordinate Descent With Variance Reduction for Composite Nonconvex Optimization](https://mlsanity.com/paper/2212.05088/) (2022)

## Abstract (arXiv)

In this work, we analyze the global convergence property of coordinate gradient descent with random choice of coordinates and stepsizes for non-convex optimization problems. Under generic assumptions, we prove that the algorithm iterate will almost surely escape strict saddle points of the objective function. As a result, the algorithm is guaranteed to converge to local minima if all saddle points are strict. Our proof is based on viewing coordinate descent algorithm as a nonlinear random dynamical system and a quantitative finite block analysis of its linearization around saddle points.