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Tikhonov regularization of a second order dynamical system with Hessian driven damping
- Source :
- Mathematical Programming
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- 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.
- Subjects :
- Hessian matrix
General Mathematics
0211 other engineering and technologies
Dynamical Systems (math.DS)
02 engineering and technology
Dynamical system
01 natural sciences
Hessian-driven damping
90C26
Tikhonov regularization
symbols.namesake
34G25, 47J25, 47H05, 90C26, 90C30, 65K10
Convergence (routing)
FOS: Mathematics
Applied mathematics
0101 mathematics
Mathematics - Dynamical Systems
Mathematics - Optimization and Control
Mathematics
65K10
021103 operations research
Full Length Paper
47J25
47H05
010102 general mathematics
Hilbert space
90C30
Function (mathematics)
Convex optimization
Optimization and Control (math.OC)
Second order dynamical system
34G25
symbols
Fast convergence methods
Convex function
Software
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Mathematical Programming
- Accession number :
- edsair.doi.dedup.....4c05bed01d94ffc883219b9f6e4f028a