English

Block Coordinate Descent Only Converge to Minimizers

Optimization and Control 2017-10-26 v1

Abstract

Given a non-convex twice continuously differentiable cost function with Lipschitz continuous gradient, we prove that all of block coordinate gradient descent, block mirror descent and proximal block coordinate descent converge to a local minimizer, almost surely with random initialization. Furthermore, we show that these results also hold true even for the cost functions with non-isolated critical points.

Keywords

Cite

@article{arxiv.1710.09047,
  title  = {Block Coordinate Descent Only Converge to Minimizers},
  author = {Enbin Song and Zhubin Shen and Qingjiang Shi},
  journal= {arXiv preprint arXiv:1710.09047},
  year   = {2017}
}

Comments

65 pages

R2 v1 2026-06-22T22:24:51.292Z