English

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 16p316p^3 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.

Keywords

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}
}
R2 v1 2026-06-22T15:21:42.192Z