Tikhonov regularization of a second order dynamical system with Hessian driven damping

We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the funct...

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Detalles Bibliográficos
Autores principales: Boţ, Radu Ioan, Csetnek, Ernö Robert, László, Szilárd Csaba
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2020
Materias:
Full Length Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550339/
https://www.ncbi.nlm.nih.gov/pubmed/34720194
http://dx.doi.org/10.1007/s10107-020-01528-8
Descripción
Sumario:We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the function values along the trajectories. The Tikhonov regularization term enables the derivation of strong convergence results of the trajectory to the minimizer of the objective function of minimum norm.

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