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Two New Weak Convergence Algorithms for Solving Bilevel Pseudomonotone Equilibrium Problem in Hilbert Space

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  • Gaobo Li
  • Sun Young Cho

Abstract

In this paper, we introduce two new subgradient extragradient algorithms to find the solution of a bilevel equilibrium problem in which the pseudomonotone and Lipschitz-type continuous bifunctions are involved in a real Hilbert space. The first method needs the prior knowledge of the Lipschitz constants of the bifunctions while the second method uses a self-adaptive process to deal with the unknown knowledge of the Lipschitz constant of the bifunctions. The weak convergence of the proposed algorithms is proved under some simple conditions on the input parameters. Our algorithms are very different from the existing related results in the literature. Finally, some numerical experiments are presented to illustrate the performance of the proposed algorithms and to compare them with other related methods.

Suggested Citation

  • Gaobo Li & Sun Young Cho, 2022. "Two New Weak Convergence Algorithms for Solving Bilevel Pseudomonotone Equilibrium Problem in Hilbert Space," Journal of Mathematics, Hindawi, vol. 2022, pages 1-16, April.
    • Handle: RePEc:hin:jjmath:2208280
    DOI: 10.1155/2022/2208280
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