广义交替近似梯度算法的线性收敛分析

On the linear convergence of the general alternating proximal gradient method for convex minimization

针对两个可分凸函数的和在线性约束下的极小化问题,在交替方向法的框架下,提出广义的交替近似梯度算法.在一定的条件下,该算法具有全局及线性收敛性.数值实验表明该算法有好的数值表现.

In this paper, we propose a general alternating proximal gradient method for linear constrained convex optimization problems with the objective containing two separable functions. Our method is based on the framework of alternating direction method of multipliers. The global and linear convergence of the proposed method is established under certain conditions. Numerical experiments show that the algorithm has good numerical performance.