Abstract
Projection-type methods are important for solving monotone linear variational inequalities. In this paper, we analyze the iteration complexity of two projection methods and accordingly establish their worst-case sublinear convergence rates measured by the iteration complexity in both the ergodic and nonergodic senses. Our analysis does not require any error bound condition or the boundedness of the feasible set, and it is scalable to other methods of the same kind.
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Acknowledgements
The authors are grateful to the anonymous referees and the editor for their valuable comments which have helped them to improve the presentation of this paper. This research was supported in part by the Natural Science Foundation of Jiangsu Province under Project No. BK20130550, the NSFC Grant 11401300, 71271112, 71390333, 70901018, 11471156 and 91530115, and the General Research Fund from Hong Kong Research Grants Council: HKBU 12302514.
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Communicated by Patrice Marcotte.
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Chen, C., Fu, X., He, B. et al. On the Iteration Complexity of Some Projection Methods for Monotone Linear Variational Inequalities. J Optim Theory Appl 172, 914–928 (2017). https://doi.org/10.1007/s10957-016-1051-6
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DOI: https://doi.org/10.1007/s10957-016-1051-6