A better convergence analysis of the block coordinate descent method for large scale machine learning
Optimization and Control
2016-08-18 v1 Numerical Analysis
Abstract
This paper considers the problems of unconstrained minimization of large scale smooth convex functions having block-coordinate-wise Lipschitz continuous gradients. The block coordinate descent (BCD) method are among the first optimization schemes suggested for solving such problems \cite{nesterov2012efficiency}. We obtain a new lower (to our best knowledge the lowest currently) bound that is times smaller than the best known on the information-based complexity of BCD method based on an effective technique called Performance Estimation Problem (PEP) proposed by Drori and Teboulle \cite{drori2012performance} recently for analyzing the performance of first-order black box optimization methods. Numerical test confirms our analysis.
Cite
@article{arxiv.1608.04826,
title = {A better convergence analysis of the block coordinate descent method for large scale machine learning},
author = {Ziqiang Shi and Rujie Liu},
journal= {arXiv preprint arXiv:1608.04826},
year = {2016}
}