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

• Published in: Journal of global optimization Vol. 84; no. 3; pp. 563 - 589
• Main Authors: Apidopoulos, Vassilis, Ginatta, Nicolò, Villa, Silvia
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2022; Springer; Springer Nature B.V
• Subjects: Algorithms; Computer Science; Convergence; Convex analysis; Convexity; Damping; Dynamical systems; Hilbert space; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; R&D; Real Functions; Research & development; Non-convex optimization; Inertial dynamics; 65L70; Rates of convergence; Heavy-ball method; Polyak–Łojasiewicz condition; 90C26; 46N10; Smooth optimization; 34D05

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...