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An Armijo-type method for pseudomonotone equilibrium problems and its applications

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  • P. Anh
  • H. Le Thi

Abstract

We present a new algorithm for solving equilibrium problems, where the underlying bifunctions are pseudomonotone and not necessarily Lipschitz-type continuous. The algorithm is based on the auxiliary problem principle and the Armijo-type linesearch techniques. Convergence properties of the algorithms are established, among them the global convergence is proved under few assumptions. Applications to generalized variational inequalities and some numerical results are reported. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • P. Anh & H. Le Thi, 2013. "An Armijo-type method for pseudomonotone equilibrium problems and its applications," Journal of Global Optimization, Springer, vol. 57(3), pages 803-820, November.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:3:p:803-820
    DOI: 10.1007/s10898-012-9970-8
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    References listed on IDEAS

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    1. P. N. Anh & L. D. Muu & V. H. Nguyen & J. J. Strodiot, 2005. "Using the Banach Contraction Principle to Implement the Proximal Point Method for Multivalued Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 124(2), pages 285-306, February.
    2. M. A. Noor, 2004. "Auxiliary Principle Technique for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 371-386, August.
    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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    Citations

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    Cited by:

    1. Jean Strodiot & Phan Vuong & Thi Nguyen, 2016. "A class of shrinking projection extragradient methods for solving non-monotone equilibrium problems in Hilbert spaces," Journal of Global Optimization, Springer, vol. 64(1), pages 159-178, January.
    2. Pham Ngoc Anh & Qamrul Hasan Ansari & Ho Phi Tu, 2023. "DC auxiliary principle methods for solving lexicographic equilibrium problems," Journal of Global Optimization, Springer, vol. 85(1), pages 129-153, January.
    3. Gaobo Li & Yanxia Lu & Yeol Je Cho, 2019. "Viscosity extragradient method with Armijo linesearch rule for pseudomonotone equilibrium problem and fixed point problem in Hilbert spaces," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(4), pages 903-921, December.
    4. Suthep Suantai & Narin Petrot & Manatchanok Khonchaliew, 2021. "Inertial Extragradient Methods for Solving Split Equilibrium Problems," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
    5. P. Anh & T. Hai & P. Tuan, 2016. "On ergodic algorithms for equilibrium problems," Journal of Global Optimization, Springer, vol. 64(1), pages 179-195, January.
    6. Pham Ngoc Anh & Qamrul Hasan Ansari, 2021. "Auxiliary Principle Technique for Hierarchical Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 882-912, March.

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    More about this item

    Keywords

    Equilibrium problems; Pseudomonotone; Global convergence; Armijo-type method; 65 K10; 90 C25;
    All these keywords.

    JEL classification:

    • K10 - Law and Economics - - Basic Areas of Law - - - General (Constitutional Law)
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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