Abstract
In this paper, we propose a projection based Newton-type algorithm for solving the variational inequality problems. A comprehensive study is conducted to analyze both global and local convergence properties of the algorithm. In particular, the algorithm is shown to be of superlinear convergence when the solution is a regular point. In addition, when the Jacobian matrix of the underlying function is positive definite at the solution or the solution is a non-degenerate point, the algorithm still possesses its superlinear convergence. Compared to the relevant projection algorithms in literature, the proposed algorithm is of remarkable advantages in terms of its generalization and favorable convergence properties under relaxed assumptions.
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The authors thank the anonymous reviewers for the insightful and constructive comments and suggestions, which helped to improve the presentation of the paper.
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This project is supported by National Natural Science Foundation of China (No. 11271226), and the Natural Science Foundation of Shandong Province (No. ZR2018MA019).
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Qu, B., Wang, C. & Meng, F. Convergence analysis of a projection algorithm for variational inequality problems. J Glob Optim 76, 433–452 (2020). https://doi.org/10.1007/s10898-019-00848-0
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DOI: https://doi.org/10.1007/s10898-019-00848-0