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Unified Framework of Extragradient-Type Methods for Pseudomonotone Variational Inequalities

Author

Listed:
  • Y. J. Wang

    (Institute of Operations Research
    Department of Mathematics Nanjing Normal University)

  • N. H. Xiu

    (Northern Jiaotong University)

  • C. Y. Wang

    (Qufu Normal University)

Abstract

In this paper, we propose a unified framework of extragradient-type methods for solving pseudomonotone variational inequalities, which allows one to take different stepsize rules and requires the computation of only two projections at each iteration. It is shown that the modified extragradient method of Ref. 1 falls within this framework with a short stepsize and so does the method of Ref. 2 with a long stepsize. It is further demonstrated that the algorithmic framework is globally convergent under mild assumptions and is sublinearly convergent if in addition a projection-type error bound holds locally. Preliminary numerical experiments are reported.

Suggested Citation

  • Y. J. Wang & N. H. Xiu & C. Y. Wang, 2001. "Unified Framework of Extragradient-Type Methods for Pseudomonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 111(3), pages 641-656, December.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:3:d:10.1023_a:1012606212823
    DOI: 10.1023/A:1012606212823
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    References listed on IDEAS

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    1. I. V. Konnov, 1997. "A Class of Combined Iterative Methods for Solving Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 94(3), pages 677-693, September.
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    Cited by:

    1. Yiran He, 2017. "Solvability of the Minty Variational Inequality," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 686-692, September.
    2. Ming Lei & Yiran He, 2021. "An Extragradient Method for Solving Variational Inequalities without Monotonicity," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 432-446, February.
    3. Jean Strodiot & Thi Nguyen & Van Nguyen, 2013. "A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems," Journal of Global Optimization, Springer, vol. 56(2), pages 373-397, June.
    4. Minglu Ye & Yiran He, 2015. "A double projection method for solving variational inequalities without monotonicity," Computational Optimization and Applications, Springer, vol. 60(1), pages 141-150, January.
    5. Y. J. Wang & N. H. Xiu & J. Z. Zhang, 2003. "Modified Extragradient Method for Variational Inequalities and Verification of Solution Existence," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 167-183, October.

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