The heavy ball with friction dynamical system for convex constrained minimization problems
Lecture Notes in Economics and Mathematical Systems.
| dc.creator | Alvarez, F. | |
| dc.creator | Attouch, H. | |
| dc.date | 2020-08-14T20:43:06Z | |
| dc.date | 2022-07-08T20:16:28Z | |
| dc.date | 2020-08-14T20:43:06Z | |
| dc.date | 2022-07-08T20:16:28Z | |
| dc.date | 2000 | |
| dc.date.accessioned | 2023-08-22T06:25:51Z | |
| dc.date.available | 2023-08-22T06:25:51Z | |
| dc.identifier | 15000001 | |
| dc.identifier | 15000001 | |
| dc.identifier | https://hdl.handle.net/10533/245948 | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/8327853 | |
| dc.description | The “heavy ball with friction” dynamical system u¨+γu˙+∇Φ(u)=0 is a non-linear oscillator with damping (γ > 0). In [2], Alvarez proved that when H is a real Hilbert space and Ф : H → ℝ is a smooth convex function whose minimal value is achieved, then each trajectory t → u (t) of this system weakly converges towards a minimizer of Ф. We prove a similar result in the convex constrained case by considering the corresponding gradient-projection dynamical system u¨+γu˙+u−projC(u−μ∇Φ(u))=0, , where C is a closed convex subset of H. This result holds when H is a possibly infinite dimensional space, and extends, by using different technics, previous results by Antipin [1]. | |
| dc.description | CMM | |
| dc.description | FONDAP | |
| dc.description | FONDAP | |
| dc.language | eng | |
| dc.relation | instname: ANID | |
| dc.relation | reponame: Repositorio Digital RI2.0 | |
| dc.relation | https://link.springer.com/chapter/10.1007/978-3-642-57014-8_2 | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.title | The heavy ball with friction dynamical system for convex constrained minimization problems | |
| dc.title | Lecture Notes in Economics and Mathematical Systems. | |
| dc.type | Articulo | |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion |