Tikhonov regularization of a perturbed heavy ball system with vanishing damping

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,
Romanian Institute of Science and Technology

Laszlo Szilard Csaba
Universitatea Tehnica Cluj-Napoca

Keywords

convex optimization; heavy ball method; continuous second order dynamical system; Tikhonov regularization;  convergence rate; strong convergence

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C.D. Alecsa, L.S. Csaba, Tikhonov regularization of a perturbed heavy ball system with vanishing damping, http://doi.org/10.13140/RG.2.2.29212.92801

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