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


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.

SUBMITTER: Bot RI 

PROVIDER: S-EPMC7077366 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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

Boţ Radu Ioan RI   Csetnek Ernö Robert ER   László Szilárd Csaba SC  

Applicable analysis 20180709 3


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 form  ...[more]

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