Abstract
This paper deals with aa perturbed heavy ball system with vanishing damping that contains a Tikhonov regularization term, in connection to the minimization problem of a convex Fréchet differentiable function. We show that the value of the objective function in a generated trajectory converges in order o (1/t2) to the global minimum of the objective function. We also obtain the fast convergence of the velocities towards zero. Moreover, we obtain that a trajectory generated by the dynamical system converges weakly to a minimizer of the objective function. Finally, we show that the presence of the Tikhonov regularization term assures the strong convergence of the generated trajectories to an element of minimal norm from the argmin set of the objective function.
Authors
Cristian Daniel Alecsa,
(“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy,
Romanian Institute of Science and Technology)
Note on author affiliation
The paper has been elaborated by the first author while working at ICTP, according to the version of the preprint posted on ResearchGate, at http://doi.org/10.13140/RG.2.2.29212.92801.
However, for the final/published version of the paper, the first author has deleted his affiliation at ICTP.
Keywords
convex optimization; heavy ball method; continuous second order dynamical system; Tikhonov regularization; convergence rate; strong convergence
Preprint available at http://doi.org/10.13140/RG.2.2.29212.92801, where the first author is affiliated at ICTP.
Cite this paper as:
C.D. Alecsa, L.S. Csaba, Tikhonov regularization of a perturbed heavy ball system with vanishing damping, SIAM J. Optim., 31 (2021) no. 4, pp. 2921-2954, http://doi.org/10.1137/20M1382027
About this paper
Journal
SIAM J. Optim.
Publisher Name
SIAM
DOI
published version: http://doi.org/10.1137/20M1382027
preprint version: DOI: 10.13140/RG.2.2.29212.92801
Print ISSN
1052-6234
Online ISSN
1095-7189
Google Scholar Profile
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