A Bregman subgradient extragradient method with self-adaptive technique for solving variational inequalities in reflexive Banach spaces

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 self-adaptive Bregman subgradient extragradient method for solving variational inequalities in the framework of a reflexive Banach space. The step-adaptive strategy avoids the difficult task of choosing a stepsize based on the Lipschitz constant of the cost function of the variational inequalities and improves the performance of the algorithm. Moreover, the use of the Bregman distance technique allows the consideration of a general feasible set for the problem. Under some suitable conditions, we prove some weak and strong convergence results for the sequence generated by the algorithm without prior knowledge of the Lipschitz constant. We further provide an application to contact problems and some numerical experiments to illustrate the performance of the algorithm.

Original languageEnglish
JournalOptimization
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • 47H09
  • 49J25
  • 65K10
  • 90C25
  • Bregman distance
  • extragradient method
  • pseudomonotone operators
  • self-adaptive stepsize
  • variational inequalities

Fingerprint

Dive into the research topics of 'A Bregman subgradient extragradient method with self-adaptive technique for solving variational inequalities in reflexive Banach spaces'. Together they form a unique fingerprint.

Cite this