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Tikhonov Regularization of a Perturbed Heavy Ball System with Vanishing Damping

This paper examines a 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 the generated trajectories converges in order o(1/t2) to the global minimum of the objective function. We also obtain fast convergence of the velocities towards zero. Moreover, we ascertain that the trajectories generated by the dynamical system converge weakly to a minimizer of the objective function. Finally, we show that the presence of the Tikhonov regularization term ensures strong convergence of the generated trajectories to the element of minimal norm from the argmin set of the objective function.

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Informasi Detail

Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.31 No.4 October-December 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 2921-2954

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

CONVEX OPTIMIZATION
TIKHONOV REGULARIZATION
CONVERGENCE RATE
STRONG CONVERGENCE
HEAVY BALL METHOD
CONTINUOUS SECOND ORDER DYNAMICAL SYSTEM

Info Detail Spesifik

https://doi.org/10.1137/20M1382027

Pernyataan Tanggungjawab

Cristian Daniel Alecsa, Szilárd Csaba László

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