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A Class of Combined Iterative Methods for Solving Variational Inequalities

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  • I. V. Konnov

    (Kazan University)

Abstract

A general approach to constructing iterative methods that solve variational inequalities is proposed. It is based on combining, modifying, and extending ideas contained in various Newton-like methods. Various algorithms can be obtained with this approach. Their convergence is proved under weak assumptions. In particular, the main mapping need not be monotone. Some rates of convergence are also given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:3:d:10.1023_a:1022605117998
    DOI: 10.1023/A:1022605117998
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    References listed on IDEAS

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    1. I. V. Konnov & S. Schaible & J. C. Yao, 2005. "Combined Relaxation Method for Mixed Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 126(2), pages 309-322, August.
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    Cited by:

    1. Jiapeng Yan & Huifang Kong & Zhihong Man, 2022. "Recurrent Neural Network-Based Nonlinear Optimization for Braking Control of Electric Vehicles," Energies, MDPI, vol. 15(24), pages 1-17, December.
    2. 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.
    3. 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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