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A new low-cost feasible projection algorithm for pseudomonotone variational inequalities

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Abstract

In this paper, we design a low-cost feasible projection algorithm for variational inequalities by replacing the projection onto the feasible set with the projection onto a ball. In each iteration, it only needs to calculate the value of the mapping once, and the projection onto the ball contained in the feasible set (which has an explicit expression), so the algorithm is easier to implement and feasible. The convergence of the algorithm is proved when the Slater condition holds for the feasible set and the mapping is pseudomonotone, Lipschitz continuous. Finally, some numerical examples are given to illustrate the effectiveness of the algorithm.

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Acknowledgements

The author appreciates the valuable comments of anonymous referees which helped to improve the quality of this paper.

Funding

The first author was supported partly by the National Natural Science Foundation of China (11901414). The third author was supported partly by the National Natural Science Foundation of China (11871359).

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Authors and Affiliations

  1. Department of Mathematics, Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu, 610066, Sichuan, People’s Republic of China

    Yongle Zhang, Limei Feng & Yiran He

Authors
  1. Yongle Zhang
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  2. Limei Feng
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  3. Yiran He
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Contributions

Yongle Zhang and Limei Feng wrote the main manuscript text, Yiran He provided the source of the problem, and Limei Feng prepared all figures. All authors reviewed the manuscript.

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Correspondence to Yongle Zhang.

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Zhang, Y., Feng, L. & He, Y. A new low-cost feasible projection algorithm for pseudomonotone variational inequalities. Numer Algor 94, 1031–1054 (2023). https://doi.org/10.1007/s11075-023-01622-w

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