Convergence analysis of a projection algorithm for variational inequality problems
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...
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| Veröffentlicht in: | Journal of global optimization 2020-02, Vol.76 (2), p.433-452 |
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| container_title | Journal of global optimization |
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| creator | Qu, Biao Wang, Changyu Meng, Fanwen |
| description | 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. |
| doi_str_mv | 10.1007/s10898-019-00848-0 |
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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.</description><identifier>ISSN: 0925-5001</identifier><identifier>EISSN: 1573-2916</identifier><identifier>DOI: 10.1007/s10898-019-00848-0</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algorithms ; Comparative analysis ; Computer Science ; Convergence ; Jacobi matrix method ; Jacobian matrix ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Nonlinear programming ; Operations Research/Decision Theory ; Optimization ; Projection ; Real Functions</subject><ispartof>Journal of global optimization, 2020-02, Vol.76 (2), p.433-452</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2019</rights><rights>COPYRIGHT 2020 Springer</rights><rights>Journal of Global Optimization is a copyright of Springer, (2019). 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| subjects | Algorithms Comparative analysis Computer Science Convergence Jacobi matrix method Jacobian matrix Mathematical analysis Mathematics Mathematics and Statistics Nonlinear programming Operations Research/Decision Theory Optimization Projection Real Functions |
| title | Convergence analysis of a projection algorithm for variational inequality problems |
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