Abstract
We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system of proximal-gradient type stated in connection with the minimization of the sum of a nonsmooth convex and a (possibly nonconvex) smooth function. The convergence of the generated trajectory to a critical point of the objective is ensured provided a regularization of the objective function satisfies the Kurdyka–Łojasiewicz property. We also provide convergence rates for the trajectory formulated in terms of the Łojasiewicz exponent.
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Radu Ioan Boţ: Research partially supported by FWF (Austrian Science Fund), project I 2419-N32.
Ernö Robert Csetnek: Research partially supported by FWF (Austrian Science Fund), project P 29809-N32 and by an Advanced Fellowship STAR-UBB of Babeş-Bolyai University, Cluj Napoca.
Szilárd Csaba László: This work was supported by a grant of Ministry of Research and Innovation, CNCS - UEFISCDI, project number PN-III-P4-ID-PCE-2016-0190, within PNCDI III.
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Boţ, R.I., Csetnek, E.R. & László, S.C. Approaching nonsmooth nonconvex minimization through second-order proximal-gradient dynamical systems. J. Evol. Equ. 18, 1291–1318 (2018). https://doi.org/10.1007/s00028-018-0441-7
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DOI: https://doi.org/10.1007/s00028-018-0441-7