Generalized viscosity inertial Tseng's method with adaptive step sizes for solving pseudomonotone variational inequalities with fixed point constraints

O. T. Mewomo*, O. J. Ogunsola, T. O. Alakoya

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study the problem of finding a solution of a pseudomonotone variational inequality problem with the constraints of fixed points of a finite family of demicontractive multivalued mappings. We introduce a new generalized viscosity inertial Tseng's extragradient method which uses self-adaptive step sizes. Unlike some existing results in this direction, we prove our strong convergence theorems without the sequentially weakly continuity condition of the pseudomonotone operator and without the knowledge of Lipschitz constants. Moreover, our strong convergence results do not follow the conventional "two cases"approach, which was often employed in proving strong convergence. Finally, we apply our result to convex minimization problems and present several numerical experiments to illustrate the performance of the proposed algorithms in comparison with other existing methods in the literature.

Original languageEnglish
Pages (from-to)193-215
Number of pages23
JournalApplied Set-Valued Analysis and Optimization
Volume6
Issue number2
Early online date27 Mar 2024
DOIs
Publication statusEarly online date - 27 Mar 2024
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2024 Applied Set-Valued Analysis and Optimization.

Keywords

  • Demicontractive multivalued mappings
  • Inertial algorithm
  • Self-adaptive step size
  • Variational inequality problem

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Mathematics (miscellaneous)
  • Modelling and Simulation
  • Control and Optimization
  • Applied Mathematics

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