A Rate of Convergence for Two-Block Coordinate Descent

TL;DR

This paper provides a simple, non-asymptotic convergence rate proof for two-block coordinate descent, filling a gap in the literature with a general result that was not previously explicitly stated.

Contribution

It offers a straightforward non-asymptotic convergence rate proof for two-block coordinate descent, a result not explicitly documented before.

Findings

Non-asymptotic convergence rate established

Proof derived from existing literature results

General form of the result is novel

Abstract

This short report gives a non-asymptotic rate of convergence proof for solving a two-block coordinate descent problem. This non-asymptotic proof is a simple result that can be derived easily from available results in the literature. We give the results in this report because in this general form we have not seen being stated in the literature.