Modified inertial subgradient extragradient method for equilibrium problems

Lateef Olakunle Jolaoso, Yekini Shehu*, Regina N. Nwokoye

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The subgradient extragradient method with inertial extrapolation step x n + θ n (x n - xn-1) (also known as inertial subgradient extragradient method) has been studied extensively in the literature for solving variational inequalities and equilibrium problems. Most of the inertial subgradient extragradient methods in the literature for both variational inequalities and equilibrium problems have not considered the special case when the inertial factor θ n = 1. The convergence results have always been obtained when the inertial factor θ n is assumed 0 ≤ θ n < 1. This paper considers the relaxed inertial version of subgradient extragradient method for equilibrium problems with 0 ≤ θ n ≤ 1. We give both weak and strong convergence results using this inertial subgradient extragradient method and also give some numerical illustrations.

Original languageEnglish
JournalInternational Journal of Nonlinear Sciences and Numerical Simulation
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • Equilibrium problem
  • Hilbert spaces
  • Inertial step
  • Subgradient extragradient method
  • Weak and strong convergence

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