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

Vassilis Apidopoulos (), Nicolò Ginatta () and Silvia Villa ()
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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

Journal of Global Optimization, 2022, vol. 84, issue 3, No 2, 563-589

Abstract: 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.

Keywords: Non-convex optimization; Smooth optimization; Inertial dynamics; Heavy-ball method; Polyak–Łojasiewicz condition; Rates of convergence; 90C26; 34D05; 46N10; 65L70 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-022-01164-w

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