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Regularized Penalty Method for General Equilibrium Problems in Banach Spaces

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  • I. V. Konnov

    (Kazan Federal University)

Abstract

We consider the regularized version of the penalty method for a general equilibrium problem in a Banach space setting. We suggest weak coercivity conditions instead of (generalized) monotonicity and show that they also provide weak and strong convergence properties of the method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:2:d:10.1007_s10957-014-0588-5
    DOI: 10.1007/s10957-014-0588-5
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    References listed on IDEAS

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    1. M. Bianchi & R. Pini, 2005. "Coercivity Conditions for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 79-92, January.
    2. I. Konnov, 2014. "On penalty methods for non monotone equilibrium problems," Journal of Global Optimization, Springer, vol. 59(1), pages 131-138, May.
    3. 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.
    4. I. Konnov & D. Dyabilkin, 2011. "Nonmonotone equilibrium problems: coercivity conditions and weak regularization," Journal of Global Optimization, Springer, vol. 49(4), pages 575-587, April.
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    Cited by:

    1. I. V. Konnov, 2019. "Equilibrium formulations of relative optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(1), pages 137-152, August.
    2. M. Bianchi & G. Kassay & R. Pini, 2022. "Brezis pseudomonotone bifunctions and quasi equilibrium problems via penalization," Journal of Global Optimization, Springer, vol. 82(3), pages 483-498, March.
    3. Lam Quoc Anh & Tran Quoc Duy & Le Dung Muu & Truong Van Tri, 2021. "The Tikhonov regularization for vector equilibrium problems," Computational Optimization and Applications, Springer, vol. 78(3), pages 769-792, April.

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