Inertial extragradient method via viscosity approximation approach for solving equilibrium problem in Hilbert space

L. O. Jolaoso, T. O. Alakoya, A. Taiwo, O. T. Mewomo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)

Abstract

In this paper, we propose a new viscosity type inertial extragradient method with Armijo line-search technique for approximating a common solution of equilibrium problem with pseudo-monotone bifunction and fixed points of relatively nonexpansive mapping in a real Hilbert space. Two advantages of our algorithm are that its convergence does not require the bifunction to satisfy any Lipschitz-type condition and only one strongly convex program and one projection onto the feasible set are perform at each iteration. Under some mild conditions on the control sequences, we state and prove a strong convergence theorem and also present two numerical examples to illustrate the performance of our algorithm. The results in this paper improve and generalize many recent results in this direction in the literature.

Original languageEnglish
Pages (from-to)387-412
Number of pages26
JournalOptimization
Volume70
Issue number2
DOIs
Publication statusPublished - 2021
Externally publishedYes

Keywords

  • Pseudo-monotone
  • bifunction
  • equilibrium problem
  • extragradient method
  • fixed point
  • inertial algorithm
  • numerical result
  • viscosity approximation

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