Hybrid Jacobian and Gauss-Seidel proximal block coordinate update methods for linearly constrained convex programming

Yangyang Xu

Numerical Linear Algebra mathscidoc:1912.43150

SIAM Journal on Optimization, 28, (1), 646-670, 2018
Recent years have witnessed the rapid development of block coordinate update (BCU) methods, which are particularly suitable for problems involving large-sized data and/or variables. In optimization, BCU first appears as the coordinate descent method that works well for smooth problems or those with separable nonsmooth terms and/or separable constraints. As nonseparable constraints exist, BCU can be applied under primal-dual settings. In the literature, it has been shown that for weakly convex problems with nonseparable linear constraints, BCU with fully Gauss--Seidel updating rule may fail to converge and that with fully Jacobian rule can converge sublinearly. However, empirically the method with Jacobian update is usually slower than that with Gauss--Seidel rule. To maintain their advantages, we propose a hybrid Jacobian and Gauss--Seidel BCU method for solving linearly constrained multiblock
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@inproceedings{yangyang2018hybrid,
  title={Hybrid Jacobian and Gauss-Seidel proximal block coordinate update methods for linearly constrained convex programming},
  author={Yangyang Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112557785191710},
  booktitle={SIAM Journal on Optimization},
  volume={28},
  number={1},
  pages={646-670},
  year={2018},
}
Yangyang Xu. Hybrid Jacobian and Gauss-Seidel proximal block coordinate update methods for linearly constrained convex programming. 2018. Vol. 28. In SIAM Journal on Optimization. pp.646-670. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112557785191710.
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