A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in hilbert space

L. O. Jolaoso, H. A. Abass, O. T. Mewomo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In this paper, we study the strong convergence of the proximal gradient algorithm with inertial extrapolation term for solving classical minimization problem and finding the fixed points of δ-demimetric mapping in a real Hilbert space. Our algorithm is inspired by the inertial proximal point algorithm and the viscosity approximation method of Moudafi. A strong convergence result is achieved in our result without necessarily imposing ∞ the summation condition n=1βn‖xn−1 − xn‖ < +∞ on the inertial term. Finally, we provide some applications and numerical example to show the efficiency and accuracy of our algorithm. Our results improve and complement many other related results in the literature.

Original languageEnglish
Pages (from-to)167-194
Number of pages28
JournalArchivum Mathematicum
Volume55
Issue number3
DOIs
Publication statusPublished - 2019
Externally publishedYes

Keywords

  • Demimetric mappings
  • Fixed point theory
  • Inertial algorithm
  • Meir Keeler contraction
  • Proximal operator
  • Viscosity approximation
  • proximal gradient algorithm

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