Tikhonov-like regularization of dynamical systems associated with nonexpansive operators defined in closed and convex sets

2019/04/11 by Pedro Pérez-Aros, Pérez-Aros, Pedro, Emilio Vilches +1 · 1 citation
Computer Science · Engineering · Mathematics · #34G25 - 47A52 - 47H05 - 47J35 - 90C25 #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stability and Controllability of Differential Equations #math.OC #msc:34G25 #msc:47A52 #msc:47H05 #msc:47J35 #msc:90C25

paper · pdf · doi:10.48550/arxiv.1904.05718

14 pages

openalex publication_date 2019/04/11 · arxiv created 2020/07/22 · arxiv updated 2020/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose a Tikhonov-like regularization for dynamical systems associated with non-expansive operators defined in closed and convex sets of a Hilbert space. We prove the well-posedness and the strong convergence of the proposed dynamical systems to a fixed point of the non-expansive operator. We apply the obtained result to dynamical system associated with the problem of finding the zeros of the sum of a cocoercive operator with the subdifferential of a convex function.

Citations

• The Baillon-Haddad Theorem Revisited
• An enhanced Baillon-Haddad theorem for convex functions on convex sets

Cited by

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

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