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

Authors:
Radu Ioan Boţ Ernö Robert Csetnek Szilárd Csaba László

Appl Anal 2020 9;99(3):361-378. Epub 2018 Jul 9.

Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca, Romania.

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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http://dx.doi.org/10.1080/00036811.2018.1495330DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7077366PMC
July 2018

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