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Combined Relaxation Methods for Generalized Monotone Variational Inequalities

In: Generalized Convexity and Related Topics

Author

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  • Igor V. Konnov

    (Kazan University)

Abstract

Summary The paper is devoted to the combined relaxation approach to constructing solution methods for variational inequalities. We describe the basic idea of this approach and implementable methods both for single-valued and for multi-valued problems. All the combined relaxation methods are convergent under very mild assumptions. This is the case if there exists a solution to the dual formulation of the variational inequality problem. In general, these methods attain a linear rate of convergence. Several classes of applications are also described.

Suggested Citation

  • Igor V. Konnov, 2007. "Combined Relaxation Methods for Generalized Monotone Variational Inequalities," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 3-31, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-37007-9_1
    DOI: 10.1007/978-3-540-37007-9_1
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    Citations

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    Cited by:

    1. I. V. Konnov, 2014. "Right-Hand Side Decomposition for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 221-238, January.
    2. Tran Quoc & Le Muu, 2012. "Iterative methods for solving monotone equilibrium problems via dual gap functions," Computational Optimization and Applications, Springer, vol. 51(2), pages 709-728, March.
    3. I. V. Konnov, 2015. "Regularized Penalty Method for General Equilibrium Problems in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 500-513, February.
    4. Tran Quoc & Pham Anh & Le Muu, 2012. "Dual extragradient algorithms extended to equilibrium problems," Journal of Global Optimization, Springer, vol. 52(1), pages 139-159, January.

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