Iterative regularization methods with new stepsize rules for solving variational inclusions

Dang Van Hieu, Pham Ky Anh, Le Dung Muu, Jean Jacques Strodiot

Research output: Contribution to journalArticlepeer-review

Abstract

The paper concerns with three iterative regularization methods for solving a variational inclusion problem of the sum of two operators, the one is maximally monotone and the another is monotone and Lipschitz continuous, in a Hilbert space. We first describe how to incorporate regularization terms in the methods of forward-backward types, and then establish the strong convergence of the resulting methods. With several new stepsize rules considered, the methods can work with or without knowing previously the Lipschitz constant of cost operator. Unlike known hybrid methods, the strong convergence of the proposed methods comes from the regularization technique. Several applications to signal recovery problems and optimal control problems together with numerical experiments are also presented in this paper. Our numerical results have illustrated the fast convergence and computational effectiveness of the new methods over known hybrid methods.

Original languageEnglish
Pages (from-to)571-599
Number of pages29
JournalJournal of Applied Mathematics and Computing
Volume68
Issue number1
DOIs
Publication statusPublished - Feb 2022

Keywords

  • Forward-backward-forward method
  • Lipschitz continuity
  • Monotonicity
  • Regularization method
  • Variational inclusion

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