INERTIAL TSENG METHOD WITH NONDECREASING ADAPTIVE STEPSIZE FOR VARIATIONAL INEQUALITY ON HADAMARD MANIFOLDS

Hammed A. Abass, Olawale K. Oyewole

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we propose an inertial and a viscosity iterative method for solving variational inequality problem on Hadamard manifolds. The iterative algorithm is inspired by Tseng’s extragradient method with a self-adaptive procedure which generates dynamic step-sizes converging to a positive constant. The proposed method does not require the knowledge of the Lipschitz constant as well as the sequential weak continuity of the corresponding operator. Under a pseudomono-tone assumption on the underlying vector field, we establish a convergence result for solving a pseudomonotone variational inequality and fixed point problems of nonexpansive mapping under some mild assump-tions. Finally, we present some fundamental experiment to illustrate the numerical behavior of our proposed method. The result discussed in this article extends and complements many related results in the literature.

Original languageEnglish
Pages (from-to)178-199
Number of pages22
JournalProceedings of the Institute of Mathematics and Mechanics
Volume50
Issue number2
DOIs
Publication statusPublished - 2024
Externally publishedYes

Keywords

  • Hadamard mani-fold
  • Riemannian manifold
  • Tseng’s method
  • self-adaptive method
  • variational inequality problem

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