Strongly Convergent Inertial Proximal Point Algorithm Without On-line Rule

Lateef O. Jolaoso, Yekini Shehu*, Jen Chih Yao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We present a strongly convergent Halpern-type proximal point algorithm with double inertial effects to find a zero of a maximal monotone operator in Hilbert spaces. The strong convergence results are obtained without on-line rule of the inertial parameters and the iterates. This makes our proof arguments different from what is obtainable in the literature where on-line rule is imposed on a strongly convergent proximal point algorithm with inertial extrapolation. Numerical examples with applications to image restoration and compressed sensing show that our proposed algorithm is useful and has practical advantages over existing ones.

Original languageEnglish
Pages (from-to)555-584
Number of pages30
JournalJournal of Optimization Theory and Applications
Volume200
Issue number2
DOIs
Publication statusPublished - Feb 2024

Keywords

  • Hilbert spaces
  • Maximal monotone operators
  • Proximal point algorithm
  • Strong convergence
  • Two-point inertia

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