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A second order dynamical approach with variable damping to nonconvex smooth minimization

Radu Ioan Bot(radu.bot***at***univie.ac.at)
Ernö Robert Csetnek(ernoe.robert.csetnek***at***univie.ac.at)
Szilard Csaba Laszlo(szilard.laszlo***at***math.utcluj.ro)

Abstract: We investigate a second order dynamical system with variable damping in connection with the minimization of a nonconvex differentiable function. The dynamical system is formulated in the spirit of the differential equation which models Nesterov's accelerated convex gradient method. We show that the generated trajectory converges to a critical point, if a regularization of the objective function satisfies the Kurdyka-Lojasiewicz property. We also provide convergence rates for the trajectory formulated in terms of the Lojasiewicz exponent.

Keywords: second order dynamical system, nonconvex optimization, Kurdyka-Lojasiewicz inequality, convergence rate

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation:

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Entry Submitted: 05/07/2018
Entry Accepted: 05/07/2018
Entry Last Modified: 05/07/2018

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