Tikhonov Regularization of a Perturbed Heavy Ball System with Vanishing Damping

Cristian Daniel Alecsa, Szilárd Csaba László

Full text: http://dx.doi.org/10.1137/20M1382027

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Abstract

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/t^2) 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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