A Strong Convergence Theorem for Solving Pseudo-monotone Variational Inequalities Using Projection Methods

Lateef Olakunle Jolaoso, Adeolu Taiwo, Timilehin Opeyemi Alakoya, Oluwatosin Temitope Mewomo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)

Abstract

Several iterative methods have been proposed in the literature for solving the variational inequalities in Hilbert or Banach spaces, where the underlying operator A is monotone and Lipschitz continuous. However, there are very few methods known for solving the variational inequalities, when the Lipschitz continuity of A is dispensed with. In this article, we introduce a projection-type algorithm for finding a common solution of the variational inequalities and fixed point problem in a reflexive Banach space, where A is pseudo-monotone and not necessarily Lipschitz continuous. Also, we present an application of our result to approximating solution of pseudo-monotone equilibrium problem in a reflexive Banach space. Finally, we present some numerical examples to illustrate the performance of our method as well as comparing it with related method in the literature.

Original languageEnglish
Pages (from-to)744-766
Number of pages23
JournalJournal of Optimization Theory and Applications
Volume185
Issue number3
DOIs
Publication statusPublished - 1 Jun 2020
Externally publishedYes

Keywords

  • Banach space
  • Extragradient method
  • Fixed point problem
  • Iterative method
  • Projection method
  • Variational inequality

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