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