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

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...

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Bibliographic Details
Published inJournal of global optimization Vol. 84; no. 3; pp. 563 - 589
Main Authors Apidopoulos, Vassilis, Ginatta, Nicolò, Villa, Silvia
Format Journal Article
LanguageEnglish
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
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01164-w