一个结构型凸优化问题的分裂算法

A Splitting Algorithm for Three-block Convex Minimization Problems

考虑带线性约束的三块变量的凸优化模型，目标函数是可分的三个函数和．给出了一个新的分裂算法．首先，对每个块变量解极小化增广拉格朗日函数．然后，通过一个校正步得到新的迭代点．证明了新算法的整体收敛性和O（1／t）的收敛阶．

In this paper, we proposed a splitting algorithm for three-block separable convex minimization model. First, one minimizes the augmented Lagrangian with respect to each block of variables using different multipliers. Secondly, a simple correction step is performed to obtain new iterate. Theoretically, we proved the global convergence and the worst-case convergence rate for this method.