FORWARD-BACKWARD SPLITTING ALGORITHM WITH SELF-ADAPTIVE METHOD FOR FINITE FAMILY OF SPLIT MINIMIZATION AND FIXED POINT PROBLEMS IN HILBERT SPACES

Hammed A. Abass, Kazeem O. Aremu, Olewale K. Oyewole, Akindele A. Mebawondu, Ojen K. Narain

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce an inertial forward-backward splitting method together with a Halpern iterative algorithm for approximating a common solution of a finite family of split minimization problem involving two proper, lower semicontinuous and convex functions and fixed point problem of a nonex-pansive mapping in real Hilbert spaces. Under suitable conditions, we proved that the sequence generated by our algorithm converges strongly to a solution of the aforementioned problems. The stepsizes studied in this paper are de-signed in such a way that they do not require the Lipschitz continuity condition on the gradient and prior knowledge of operator norm. Finally, we illustrate a numerical experiment to show the performance of the proposed method. The result discussed in this paper extends and complements many related results in literature.

Original languageEnglish
Pages (from-to)109-127
Number of pages19
JournalJournal of Numerical Analysis and Approximation Theory
Volume52
Issue number2
DOIs
Publication statusPublished - 28 Dec 2023
Externally publishedYes

Keywords

  • Nonexpansive mapping
  • fixed point problem
  • forward-backward splitting method
  • inertial method
  • minimization problem

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