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The PPA-based numerical algorithm with the \(O(1/t)\) convergence rate for variant variational inequalities

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Abstract

Since proximal point algorithms (PPAs) are attractive for solving monotone variational inequalities, various versions of PPAs are developed for variant variational inequalities. In this paper, we prove a worst-case \(O(1/t)\) convergence rate in an ergodic sense for the PPA-based numerical algorithm in literature. Some numerical results are also reported to verify the computational preference.

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Acknowledgments

The authors are grateful to the associate editor and anonymous referees for their valuable comments which have helped us greatly improve the presentation of this paper. This work was supported by National Natural Science Foundation of China (Grant No. 11001053), Natural Science Foundation of Jiangsu Province, China (Grant No. BK2012662) and Qing Lan Project.

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Correspondence to Min Li.

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Li, M., Jiang, Z. The PPA-based numerical algorithm with the \(O(1/t)\) convergence rate for variant variational inequalities. Optim Lett 8, 1487–1500 (2014). https://doi.org/10.1007/s11590-013-0674-x

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