A second-order dynamical approach with variable damping to nonconvex smooth minimization
Radu Ioan Boţ1, Ernö Robert Csetnek1, Szilárd Csaba László2
1Faculty of Mathematics, University of Vienna, Vienna, Austria.
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.
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