A Double Projection Algorithm for Solving Non-Monotone Variational Inequalities

WANG Xiaoting; LONG Xianjun; PENG Zaiyun

doi:10.21656/1000-0887.420414

Volume 43 Issue 8

Aug. 2022

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WANG Xiaoting, LONG Xianjun, PENG Zaiyun. A Double Projection Algorithm for Solving Non-Monotone Variational Inequalities[J]. Applied Mathematics and Mechanics, 2022, 43(8): 927-934. doi: 10.21656/1000-0887.420414

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A Double Projection Algorithm for Solving Non-Monotone Variational Inequalities

doi: 10.21656/1000-0887.420414

1.
School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P.R.China
2.
School of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, P.R.China

Received Date: 2021-12-31
Rev Recd Date: 2022-03-23

Available Online: 2022-06-21

Publish Date: 2022-08-01

Abstract

Abstract

The projection algorithm is one of the main methods to solve variational inequality problems. At present, the research on projection algorithms usually requires the assumptions that the mapping is monotone and Lipschitz continuous, but in practical problems, these assumptions are often unsatisfied. A new double projection algorithm for solving non-monotone variational inequality problems was proposed with the line search method. Under the assumption that the mapping is uniformly continuous, the sequence generated by the algorithm was proved to strongly converge to the solution of the variational inequality. The numerical experiments illustrate the effectiveness and superiority of the proposed algorithm.
- variational inequality,
- double projection algorithm,
- uniformly continuous,
- non-monotone,
- strong convergence

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References

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