Block coordinate proximal gradient methods with variable Bregman functions for nonsmooth separable optimization
Block coordinate proximal gradient methods with variable Bregman functions for nonsmooth separable optimization
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DOI：
10.1007/s10107-015-0969-z
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发表时间：
2016-01
影响因子：
2.7
通讯作者：
Xiaoqin Hua;N. Yamashita
中科院分区：
文献类型：
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作者：
Xiaoqin Hua;N. Yamashita
本文提出了一类求解大规模非光滑可分优化问题的块坐标邻近梯度（BCPG）方法。所提出的BCPG方法基于Bregman函数，其在每次迭代中可能变化。这些方法包括许多众所周知的优化方法，例如拟牛顿法、块坐标下降法和邻近点法。对于所提出的方法，我们建立其全局收敛性时，块选择的高斯-赛德尔规则。在适当的假设下，证明了所提出的方法的收敛速度是R-线性的。我们还提出了一个新的BCPG方法与可变核的可分离的单纯形约束的凸问题的数值结果。
In this paper, we propose a class of block coordinate proximal gradient (BCPG) methods for solving large-scale nonsmooth separable optimization problems. The proposed BCPG methods are based on the Bregman functions, which may vary at each iteration. These methods include many well-known optimization methods, such as the quasi-Newton method, the block coordinate descent method, and the proximal point method. For the proposed methods, we establish their global convergence properties when the blocks are selected by the Gauss–Seidel rule. Further, under some additional appropriate assumptions, we show that the convergence rate of the proposed methods is R-linear. We also present numerical results for a new BCPG method with variable kernels for a convex problem with separable simplex constraints.