求解可分离凸优化问题的非精确混合分裂算法

An inexact hybrid splitting method for separable convex optimization

针对一类有四个块变量的可分离凸优化问题,提出一种非精确混合分裂算法.在每一轮迭代中,该算法需要求解四个子问题,根据子问题计算工作量的大小,将四个子问题分为两组,每组包含工作量相当的两个子问题.算法在组内执行平行分裂方法,两组间执行交替方向方法,并允许迭代子问题的非精确求解.在适当的条件下,证明了所提出的混合分裂算法具有全局收敛性.

For a separable convex optimization with four block-variables,this paper proposes an inexact hybrid splitting method. At each iteration of the proposed method,four subproblems need to be solved. It partitions them into two groups based on the view of computational point. A parallel splitting method is performed in a group,while an alternating direction method is performed between the groups. All iteration subproblems admit inexact solution. This paper proves global convergence of the proposed method under some suitable conditions.