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Article Dans Une Revue Advances in Nonlinear Analysis Année : 2021

Inducing strong convergence of trajectories in dynamical systems associated to monotone inclusions with composite structure

Résumé

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 Krasnoselskiĭ-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.

Dates et versions

hal-03429962 , version 1 (16-11-2021)

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Radu Ioan Boţ, Sorin-Mihai Grad, Dennis Meier, Mathias Staudigl. Inducing strong convergence of trajectories in dynamical systems associated to monotone inclusions with composite structure. Advances in Nonlinear Analysis, 2021, 10 (1), pp.450-476. ⟨10.1515/anona-2020-0143⟩. ⟨hal-03429962⟩
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