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… Click to show full abstract
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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