A semi-proximal-based strictly contractive Peaceman-Rachford splitting method
Yan Gu, Bo Jiang, Deren Han · arXiv (Cornell University) · 2015
The Peaceman-Rachfor d splitting method is very efficient for minimizing sum of two functions each depends on its variable, and the constraint is a linear equality. However, its convergence was not guaranteed without extra requirements. Very recently, He et al. (SIAM J. Optim. 24: 1011 - 1040, 2014) proved the convergence of a strictly contractive Peaceman-Rachfor splitting method by employing a suitable underdetermined relaxation factor. In this paper, we further extend the so-called strictly contractive Peaceman-Rachfor d splitting method by using two different relaxation factors, and to make the method more exible, we introduce semi-proximal terms to the subproblems. We characterize the relation of these two factors, and show that one factor is always underdetermined while the other one is allowed to be larger than 1. Such a exible conditions makes it possible to > >