INDUCING STRONG CONVERGENCE OF TRAJECTORIES IN DYNAMICAL SYSTEMS ASSOCIATED TO MONOTONE INCLUSIONS WITH COMPOSITE STRUCTURE

Radu Bot*, Sorin Mihai Grad, Dennis Meier, Mathias Staudigl

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Web of Science)

Abstract

In this work we investigate dynamical systems designed to approach the solution sets of inclusion problems involving the sum of two maximally monotone operators. Our aim is to design methods which guarantee strong convergence of trajectories towards the minimum norm solution of the underlying monotone inclusion problem. To that end, we investigate in detail the asymptotic behavior of dynamical systems perturbed by a Tikhonov regularization where either the maximally monotone operators themselves, or the vector field of the dynamical system is regularized. In both cases we prove strong convergence of the trajectories towards minimum norm solutions to an underlying monotone inclusion problem, and we illustrate numerically qualitative differences between these two complementary regularization strategies. The so-constructed dynamical systems are either of Krasnoselskii-Mann, of forward-backward type or of forward-backward-forward type, and with the help of injected regularization we demonstrate seminal results on the strong convergence of Hilbert space valued evolutions designed to solve monotone inclusion and equilibrium problems.

Original languageEnglish
Pages (from-to)450-476
Number of pages27
JournalAdvances in Nonlinear Analysis
Volume10
Issue number1
DOIs
Publication statusPublished - Jan 2021

Keywords

  • monotone inclusions
  • dynamical systems
  • Tikhonov regularization
  • asymptotic analysis
  • ASYMPTOTIC CONVERGENCE
  • EVOLUTION-EQUATIONS
  • OPTIMIZATION
  • ALGORITHMS
  • OPERATORS
  • SUM

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