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Convergence rates for the heavy-ball continuous dynamics for non-convex optimization, under Polyak–Łojasiewicz condition

Author

Listed:
  • Vassilis Apidopoulos

    (Università degli Studi di Genova)

  • Nicolò Ginatta

    (MaLGa, DIMA, Universitá degli Studi di Genova)

  • Silvia Villa

    (MaLGa, DIMA, Universitá degli Studi di Genova)

Abstract

We study convergence of the trajectories of the Heavy Ball dynamical system, with constant damping coefficient, in the framework of convex and non-convex smooth optimization. By using the Polyak–Łojasiewicz condition, we derive new linear convergence rates for the associated trajectory, in terms of objective function values, without assuming uniqueness of the minimizer.

Suggested Citation

  • Vassilis Apidopoulos & Nicolò Ginatta & Silvia Villa, 2022. "Convergence rates for the heavy-ball continuous dynamics for non-convex optimization, under Polyak–Łojasiewicz condition," Journal of Global Optimization, Springer, vol. 84(3), pages 563-589, November.
    • Handle: RePEc:spr:jglopt:v:84:y:2022:i:3:d:10.1007_s10898-022-01164-w
    DOI: 10.1007/s10898-022-01164-w
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    References listed on IDEAS

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    1. Ion Necoara & Yurii Nesterov & François Glineur, 2019. "Linear convergence of first order methods for non-strongly convex optimization," LIDAM Reprints CORE 3000, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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