Abstract
In the literature, 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 studies the inexact version of this combination, where the resulting subproblems are allowed to be solved approximately subject to different inexactness criteria. We prove the global convergence and establish worst-case convergence rates for the derived inexact algorithms.
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Acknowledgements
The first author was supported by National Natural Science Foundation of China grant 11001053, Program for New Century Excellent Talents in University grant NCET-12-0111 and Natural Science Foundation of Jiangsu Province grant BK2012662. The second author was supported in part by Hong Kong General Research Fund grants HKBU 201409 and HKBU 201611. The third author was supported by the grant FRG2/11-12/120 from Hong Kong Baptist University and the General Research Fund HKBU 203311 from Hong Kong Research Grants Council.
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Communicated by Masao Fukushima.
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Li, M., Liao, LZ. & Yuan, X. Inexact Alternating Direction Methods of Multipliers with Logarithmic–Quadratic Proximal Regularization. J Optim Theory Appl 159, 412–436 (2013). https://doi.org/10.1007/s10957-013-0334-4
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DOI: https://doi.org/10.1007/s10957-013-0334-4