Inertial self-adaptive parallel extragradient-type method for common solution of variational inequality problems

L. O. Jolaoso*, O. K. Oyewole, K. O. Aremu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce a new inertial self-adaptive parallel subgradient extragradient method for finding common solution of variational inequality problems with monotone and Lipschitz continuous operators. The stepsize of the algorithm is updated self-adaptively at each iteration and does not involve a line search technique nor a prior estimate of the Lipschitz constants of the cost operators. Also, the algorithm does not required finding the farthest element of the finite sequences from the current iterate which has been used in many previous methods. We prove a strong convergence result and provide some applications of our result to other optimization problems. We also give some numerical experiments to illustrate the performance of the algorithm by comparing with some other related methods in the literature.

Original languageEnglish
JournalApplicable Analysis
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • Common solution
  • monotone operators
  • parallel extragradient method
  • self-adaptive
  • variational inequality

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