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arXiv · 1710.09047

Block Coordinate Descent Only Converge to Minimizers

Enbin Song·Zhubin Shen·Qingjiang Shi
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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.

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Enbin Song, Zhubin Shen, Qingjiang Shi. 2017-10-25. Block Coordinate Descent Only Converge to Minimizers. https://arxiv.org/abs/1710.09047

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