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Variance-based stochastic projection gradient method for two-stage co-coercive stochastic variational inequalities

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Abstract

The existing stochastic approximation (SA)-type algorithms for two-stage stochastic variational inequalities (SVIs) are based on the uniqueness of the second-stage solution, which restricts the use of those algorithms. In this paper, we propose a dynamic sampling stochastic projection gradient method (DS-SPGM) for solving a class of two-stage SVIs satisfying the co-coercive property. With the co-coercive property and the dynamic sampling technique, we can handle the two-stage SVIs when the second-stage problem has multiple solutions and achieve the rate of convergence with \(\varvec{O}(\varvec{1/\sqrt{K}})\). Moreover, numerical experiments show the efficiency of the DS-SPGM.

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Acknowledgements

We would like to thank the associate editor and two referees for their very helpful comments.

Funding

This research is supported by the National Key R &D Program of China (No.2023YFA1009300), the National Natural Science Foundation of China (12122108, 12261160365, and 12201084) and the China Postdoctoral Science Foundation (2023M730417).

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Authors and Affiliations

  1. Key Laboratory of NSLSCS, Ministry of Education, Jiangsu International Joint Laboratory of BDMCA, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, People’s Republic of China

    Bin Zhou, Yongzhong Song & Hailin Sun

  2. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, People’s Republic of China

    Jie Jiang

Authors
  1. Bin Zhou
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  2. Jie Jiang
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  3. Yongzhong Song
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  4. Hailin Sun
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Contributions

Bin Zhou and Hailin Sun wrote the main manuscript text. Bin Zhou has completed the numerical experiments. Jie Jiang and Yongzhong Song provided crucial assistance in proving the key theorems in this manuscript. All authors reviewed the manuscript.

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Correspondence to Hailin Sun.

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Zhou, B., Jiang, J., Song, Y. et al. Variance-based stochastic projection gradient method for two-stage co-coercive stochastic variational inequalities. Numer Algor (2024). https://doi.org/10.1007/s11075-024-01779-y

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  • DOI: https://doi.org/10.1007/s11075-024-01779-y

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