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Title of Journal: Math Program

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Abbravation: Mathematical Programming

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Springer Berlin Heidelberg

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DOI

10.1007/bf02288930

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1436-4646

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Iteration complexity analysis of block coordinate

Authors: Mingyi Hong Xiangfeng Wang Meisam Razaviyayn ZhiQuan Luo
Publish Date: 2016/08/19
Volume: 163, Issue: 1-2, Pages: 85-114
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Abstract

In this paper we provide a unified iteration complexity analysis for a family of general block coordinate descent methods covering popular methods such as the block coordinate gradient descent and the block coordinate proximal gradient under various different coordinate update rules We unify these algorithms under the socalled block successive upperbound minimization BSUM framework and show that for a broad class of multiblock nonsmooth convex problems all algorithms covered by the BSUM framework achieve a global sublinear iteration complexity of mathcalO1/r where r is the iteration index Moreover for the case of block coordinate minimization where each block is minimized exactly we establish the sublinear convergence rate of O1/r without per block strong convexity assumption

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