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Extragradient Algorithm for Solving Pseudomonotone Equilibrium Problem with Bregman Distance in Reflexive Banach Spaces

Author

Listed:
  • Lateef Olakunle Jolaoso

    (Sefako Makgatho Health Sciences University)

  • Christian Chibueze Okeke

    (University of the Witwatersrand)

  • Yekini Shehu

    (Zhejiang Normal University)

Abstract

Using the Bregman distance technique, we study the approximation of solution of pseudomonotone equilibrium problem using modified extragradient method in a real reflexive Banach space. Our proposed method involves a non-increasing self-adaptive stepsize rule and prove a weak convergence result without any prior estimate of the Lipschitz-like constants of the equilibrium bifunction under some appropriate conditions in a real reflexive Banach space. Some application to generalized Nash equilibrium problem in differential games is given. Finally, we give numerical examples to compare the performance of our method with other related methods in the literature and illustrate our method using various types of Bregman distance functions.

Suggested Citation

  • Lateef Olakunle Jolaoso & Christian Chibueze Okeke & Yekini Shehu, 2021. "Extragradient Algorithm for Solving Pseudomonotone Equilibrium Problem with Bregman Distance in Reflexive Banach Spaces," Networks and Spatial Economics, Springer, vol. 21(4), pages 873-903, December.
    • Handle: RePEc:kap:netspa:v:21:y:2021:i:4:d:10.1007_s11067-021-09554-5
    DOI: 10.1007/s11067-021-09554-5
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    References listed on IDEAS

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    1. Alfredo Iusem & Mostafa Nasri, 2011. "Korpelevich’s method for variational inequality problems in Banach spaces," Journal of Global Optimization, Springer, vol. 50(1), pages 59-76, May.
    2. Y. Censor & A. Gibali & S. Reich, 2011. "The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 318-335, February.
    3. Sergey I. Lyashko & Vladimir V. Semenov, 2016. "A New Two-Step Proximal Algorithm of Solving the Problem of Equilibrium Programming," Springer Optimization and Its Applications, in: Boris Goldengorin (ed.), Optimization and Its Applications in Control and Data Sciences, pages 315-325, Springer.
    4. Dan Butnariu & Elena Resmerita, 2006. "Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-39, February.
    5. Boţ, R.I. & Csetnek, E.R. & Vuong, P.T., 2020. "The forward–backward–forward method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces," European Journal of Operational Research, Elsevier, vol. 287(1), pages 49-60.
    6. Giancarlo Bigi & Mauro Passacantando, 2015. "Descent and Penalization Techniques for Equilibrium Problems with Nonlinear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 804-818, March.
    7. L. D. Muu & T. D. Quoc, 2009. "Regularization Algorithms for Solving Monotone Ky Fan Inequalities with Application to a Nash-Cournot Equilibrium Model," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 185-204, July.
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