A second-order dynamical approach with variable damping to nonconvex smooth minimization. Issue 3 (17th February 2020) - Boţ, Radu Ioan; Csetnek, Ernö Robert; László, Szilárd Csaba
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.