@article{a7f8785529cf45a1a7cec3721f017167,
title = "On the O(1/t) Convergence Rate of Alternating Direction Method with Logarithmic-Quadratic Proximal Regularization",
abstract = "It was shown recently that the Douglas-Rachford alternating direction method of multipliers can be combined with the logarithmic-quadratic proximal regularization for solving a class of variational inequalities with separable structures. This paper further shows a worst-case O(1/t) convergence rate for this algorithm where a general Glowinski relaxation factor is used.",
keywords = "Alternating direction method of multipliers, Convergence rate, Glowinski's relaxation factor, Logarithmic-quadratic proximal regularization, Variational inequality",
author = "Min Tao and Xiaoming Yuan",
note = "Funding information: School of Science, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210093, China (
[email protected]). This author{\textquoteright}s research was supported by the Scientific Research Foundation of Nanjing University of Posts and Telecommunicat ions (NY210049). $ Corresponding author. Department of Mathematics, Hong Kong Baptist University, Hong Kong, China (
[email protected]). This author{\textquoteright}s research was supported by the Hong Kong General Research Fund (HKBU 203311) and the HKBU FRG Fund (FRG2/11-12/120). Publisher copyright: {\textcopyright} 2012, Society for Industrial and Applied Mathematics",
year = "2012",
month = oct,
day = "31",
doi = "10.1137/110847639",
language = "English",
volume = "22",
pages = "1431--1448",
journal = "SIAM Journal on Optimization",
issn = "1052-6234",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
number = "4",
}