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Combined Relaxation Method for Monotone Equilibrium Problems

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  • I. V. Konnov

    (Kazan University)

Abstract

A scalar equilibrium problem which involves a monotone differentiable cost bifunction is considered. For such bifunction, a skew-symmetric type property with respect to the partial gradients is established. This property enables us to construct a new combined relaxation method and essentially simplify its line search procedure. An application to an inverse equilibrium problem is also presented.

Suggested Citation

  • I. V. Konnov, 2001. "Combined Relaxation Method for Monotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 327-340, November.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:2:d:10.1023_a:1011930301552
    DOI: 10.1023/A:1011930301552
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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. E. Allevi & A. Gnudi & I.V. Konnov & S. Schaible, 2003. "Noncooperative Games with Vector Payoffs Under Relative Pseudomonotonicity," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 245-254, August.
    2. Dang Hieu, 2017. "New subgradient extragradient methods for common solutions to equilibrium problems," Computational Optimization and Applications, Springer, vol. 67(3), pages 571-594, July.
    3. L. C. Zeng & J. C. Yao, 2006. "Modified Combined Relaxation Method for General Monotone Equilibrium Problems in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 469-483, December.
    4. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
    5. I.V. Konnov, 2003. "On Lexicographic Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 118(3), pages 681-688, September.
    6. I. Konnov, 2013. "Vector network equilibrium problems with elastic demands," Journal of Global Optimization, Springer, vol. 57(2), pages 521-531, October.
    7. Q.H. Ansari & I.V. Konnov & J.C. Yao, 2002. "Characterizations of Solutions for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(3), pages 435-447, June.
    8. E. Allevi & A. Gnudi & I.V. Konnov, 2004. "Generalized Vector Variational Inequalities over Countable Product of Sets," Journal of Global Optimization, Springer, vol. 30(2), pages 155-167, November.
    9. Q. H. Ansari & I. V. Konnov & J. C. Yao, 2001. "Existence of a Solution and Variational Principles for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 481-492, September.

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