@Article{JCM-41-1017,
author = {Gu , YanJiang , Bo and Han , Deren},
title = {An Indefinite-Proximal-Based Strictly Contractive Peaceman-Rachford Splitting Method},
journal = {Journal of Computational Mathematics},
year = {2023},
volume = {41},
number = {6},
pages = {1017--1040},
abstract = {<p style="text-align: justify;">The Peaceman-Rachford splitting method is efficient for minimizing a convex optimization problem with a separable objective function and linear constraints. However, its
convergence was not guaranteed without extra requirements. He et al. (SIAM J. Optim.
24: 1011-1040, 2014) proved the convergence of a strictly contractive Peaceman-Rachford
splitting method by employing a suitable underdetermined relaxation factor. In this paper,
we further extend the so-called strictly contractive Peaceman-Rachford splitting method
by using two different relaxation factors. Besides, motivated by the recent advances on the
ADMM type method with indefinite proximal terms, we employ the indefinite proximal
term in the strictly contractive Peaceman-Rachford splitting method. We show that the
proposed indefinite-proximal strictly contractive Peaceman-Rachford splitting method is
convergent and also prove the $o(1/t)$ convergence rate in the nonergodic sense. The numerical tests on the $l_1$ regularized least square problem demonstrate the efficiency of the
proposed method.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2112-m2020-0023},
url = {http://global-sci.org/intro/article_detail/jcm/22102.html}
}