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Inertial projection and contraction algorithms with larger step sizes for solving quasimonotone variational inequalities

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Abstract

This paper deals with a class of inertial projection and contraction algorithms for solving a variational inequality problem involving quasimonotone and Lipschitz continuous mappings in Hilbert spaces. The algorithms incorporate inertial techniques and the Barzilai–Borwein step size strategy, moreover their line search conditions and some parameters are relaxed to obtain larger step sizes. The weak convergence of the algorithms is proved without the knowledge of the Lipschitz constant of the mappings. Meanwhile, the nonasymptotic convergence and the linear convergence of the algorithms are established. Some numerical experiments show that the proposed algorithms are more effective than some existing ones.

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Acknowledgements

The important part of the paper was done when the first author was a visitor at Department of Statistics & Applied Probability, National University of Singapore. The first author is profoundly grateful to professor Yu Tao, for his help and encouragement. The authors are indebted to the anonymous Editor and referees for their valuable comments and suggestions which helped us very much in improving the original version of this paper. This work was supported by the National Natural Science Foundation of China (11701479, 11701478), the Chinese Postdoctoral Science Foundation (2018M643434) and the Fundamental Research Funds for the Central Universities (A0920502052101-335).

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Authors and Affiliations

  1. Department of Mathematics, Southwest Jiaotong University, Chengdu, 611756, Sichuan, China

    Zhong-bao Wang, Jiang Yi & Zhang-you Chen

  2. National Engineering Laboratory of Integrated Transportation Big Data Application Technology, Chengdu, 611756, Sichuan, China

    Zhong-bao Wang, Jiang Yi & Zhang-you Chen

  3. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, China

    Zhong-bao Wang

  4. School of Economics and Management, Southwest Jiaotong University, Chengdu, 610031, Sichuan, China

    Xue Chen

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  1. Zhong-bao Wang
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Correspondence to Zhong-bao Wang.

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Wang, Zb., Chen, X., Yi, J. et al. Inertial projection and contraction algorithms with larger step sizes for solving quasimonotone variational inequalities. J Glob Optim 82, 499–522 (2022). https://doi.org/10.1007/s10898-021-01083-2

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  • DOI: https://doi.org/10.1007/s10898-021-01083-2

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