This paper proposes a synchronous parallel block coordinate descent algorithm for minimizing a composite function, which consists of a smooth convex function plus a non-smooth but separable convex function. Due to the generalization of the proposed method, some existing synchronous parallel algorithms can be considered as special cases. To tackle high dimensional problems, the authors further develop a randomized variant, which randomly update some blocks of coordinates at each round of computation. Both proposed parallel algorithms are proven to have sub-linear convergence rate under rather mild assumptions. The numerical experiments on solving the large scale regularized logistic regression with ℓ₁ norm penalty show that the implementation is quite efficient. The authors conclude with explanation on the observed experimental results and discussion on the potential improvements.

中文翻译：

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非光滑凸函数最小化的同步并行块坐标下降法

本文提出了一种同步并行块坐标下降算法，用于使复合函数最小化，该算法由光滑凸函数和非光滑但可分离的凸函数组成。由于所提方法的一般性，可以将一些现有的同步并行算法视为特殊情况。为了解决高维问题，作者进一步开发了一个随机变量，该变量在每轮计算中都会随机更新一些坐标块。在相当温和的假设下，两种提议的并行算法均被证明具有亚线性收敛速率。with ₁求解大规模正则逻辑回归的数值实验规范惩罚表明实施非常有效。作者最后对观察到的实验结果进行了解释，并对可能的改进进行了讨论。