Year: 2023
Author: Yan Gu, Bo Jiang, Deren Han
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 6 : pp. 1017–1040
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2112-m2020-0023
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 6 : pp. 1017–1040
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Indefinite proximal Strictly contractive Peaceman-Rachford splitting method Convex minimization Convergence rate.
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