An explicit subgradient extragradient algorithm with self-adaptive stepsize for pseudomonotone equilibrium problems in Banach spaces

Lateef Olakunle Jolaoso*, Maggie Aphane

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce an explicit subgradient extragradient algorithm for solving equilibrium problem with a bifunction satisfying pseudomonotone and Lipschitz-like condition in a 2-uniformly convex and uniformly smooth Banach space. We also defined a new self-adaptive stepsize rule and prove a convergence result for solving the equilibrium problem without any prior estimate of the Lipschitz-like constants of the bifunction. Furthermore, we provide some numerical examples to illustrate the efficiency and accuracy of the proposed algorithm. This result improves and extends many recent results in this direction in the literature.

Original languageEnglish
JournalNumerical Algorithms
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • Banach spaces
  • Equilibrium problem
  • Extragradient method
  • Pseudomonotone
  • Self adaptive stepsize

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