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}
}
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65 pages