Convergence Rate Analysis for the Alternating Direction Method of Multipliers with a Substitution Procedure for Separable Convex Programming

Bingsheng He, Min Tao, Xiaoming Yuan
2017 Mathematics of Operations Research  
Recently, in [17] we have showed the first possibility of combining the Douglas-Rachford alternating direction method of multipliers (ADMM) with a Gaussian back substitution procedure for solving a convex minimization model with a general separable structure. This paper is a further study on theoretical aspects of this theme. We first derive a general algorithmic framework to combine ADMM with either a forward or backward substitution procedure. Then, we show that convergence of this framework
more » ... an be easily proved from contraction perspective, and its local linear convergence rate is provable if certain standard error bound condition is assumed. Without such an error bound assumption, we can still estimate the worst-case iteration complexity for this framework in both ergodic and nonergodic senses.
doi:10.1287/moor.2016.0822 fatcat:as2gersjdngxbg7xhg4dpa4bcy