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Convergence analysis of a projection algorithm for variational inequality problems

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  • Biao Qu

    (Qufu Normal University)

  • Changyu Wang

    (Qufu Normal University)

  • Fanwen Meng

    (Dalian Maritime University)

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.

Suggested Citation

  • Biao Qu & Changyu Wang & Fanwen Meng, 2020. "Convergence analysis of a projection algorithm for variational inequality problems," Journal of Global Optimization, Springer, vol. 76(2), pages 433-452, February.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:2:d:10.1007_s10898-019-00848-0
    DOI: 10.1007/s10898-019-00848-0
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    References listed on IDEAS

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    1. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
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