Randomized Primal-Dual Proximal Block Coordinate Updates

Xiang Gao Yangyang Xu Shuzhong Zhang

Numerical Linear Algebra mathscidoc:1912.43147

Journal of the Operations Research Society of China, 7, (2), 205--250, 2019
In this paper, we propose a randomized primaldual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints. Assuming mere convexity, we establish its <i>O</i>(1/<i>t</i>) convergence rate in terms of the objective value and feasibility measure. The framework includes several existing algorithms as special cases such as a primaldual method for bilinear saddle-point problems (PD-S), the proximal Jacobian alternating direction method of multipliers (Prox-JADMM) and a randomized variant of the ADMM for multi-block convex optimization. Our analysis recovers and/or strengthens the convergence properties of several existing algorithms. For example, for PD-S our result leads to the same order of convergence rate without the previously assumed boundedness condition on the constraint sets, and for Prox-JADMM the new
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@inproceedings{xiang2019randomized,
  title={Randomized Primal-Dual Proximal Block Coordinate Updates},
  author={Xiang Gao, Yangyang Xu, and Shuzhong Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112547469771707},
  booktitle={Journal of the Operations Research Society of China},
  volume={7},
  number={2},
  pages={205--250},
  year={2019},
}
Xiang Gao, Yangyang Xu, and Shuzhong Zhang. Randomized Primal-Dual Proximal Block Coordinate Updates. 2019. Vol. 7. In Journal of the Operations Research Society of China. pp.205--250. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112547469771707.
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