Titel
Levenberg-Marquardt Dynamics Associated to Variational Inequalities
Autor*in
Abstract
In connection with the optimization problem
infx∈argminΨ{Φ(x)+Θ(x)},
where Φ is a proper, convex and lower semicontinuous function and Θ and Ψ are convex and smooth functions defined on a real Hilbert space, we investigate the asymptotic behavior of the trajectories of the nonautonomous Levenberg-Marquardt dynamical system
{v(t)∈∂Φ(x(t))λ(t)x˙(t)+v˙(t)+v(t)+∇Θ(x(t))+β(t)∇Ψ(x(t))=0,,
where λ and β are functions of time controlling the velocity and the penalty term, respectively. We show weak convergence of the generated trajectory to an optimal solution as well as convergence of the objective function values along the trajectories, provided λ is monotonically decreasing, β satisfies a growth condition and a relation expressed via the Fenchel conjugate of Ψ is fulfilled. When the objective function is assumed to be strongly convex, we can even show strong convergence of the trajectories.
Stichwort
Nonautonomous systemsLevenberg-Marquardt dynamicsRegularized Newton-like dynamicsLyapunov analysisConvex optimizationVariational inequalitiesPenalization techniques
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
phaidra.univie.ac.at/o:715268
Erschienen in
Titel
Set-Valued and Variational Analysis
Band
25
Ausgabe
3
Seitenanfang
569
Seitenende
589
Publication
Springer Nature
Erscheinungsdatum
2017
Zugänglichkeit
Rechte
Rechteangabe
© The Author(s) 2017
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