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Modified Projection Methods for Solving Multi-valued Variational Inequality without Monotonicity

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Abstract

In this paper, we propose two new projection-type algorithms for solving the multi-valued variational inequality in finite dimensional spaces. We prove the convergence of the sequences generated by the proposed projection-type algorithms without any monotonicity. Moreover, we provide some numerical experiments to illustrate the efficiency of the proposed projection-type algorithms.

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Acknowledgements

The authors are grateful to the editors and reviewers whose helpful comments and suggestions have led to much improvement in the paper.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, People’s Republic of China

    Xin He, Nan-jing Huang & Xue-song Li

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  1. Xin He
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  2. Nan-jing Huang
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  3. Xue-song Li
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Correspondence to Nan-jing Huang.

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This work was supported by the National Natural Science Foundation of China (11471230, 11671282).

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He, X., Huang, Nj. & Li, Xs. Modified Projection Methods for Solving Multi-valued Variational Inequality without Monotonicity. Netw Spat Econ 22, 361–377 (2022). https://doi.org/10.1007/s11067-019-09485-2

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