Asymptotic for the perturbed heavy ball system with vanishing damping term

DOI10.3934/eect.2017010zbMath1366.34070arXiv1609.00135OpenAlexW2963202843MaRDI QIDQ523947

Ramzi May, Mounir Balti

Publication date: 25 April 2017

Published in: Evolution Equations and Control Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.00135

zbMATH Keywords

rate of convergenceweak convergenceasymptotic behaviorconvex functiondifferential equationenergy functionasymptotically small dissipation

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Asymptotic properties of solutions to ordinary differential equations (34D05) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Differential inequalities involving functions of a single real variable (34A40)

Related Items (15)

Convergence Rates of the Heavy Ball Method for Quasi-strongly Convex Optimization ⋮ Accelerated differential inclusion for convex optimization ⋮ On the strong convergence of the trajectories of a Tikhonov regularized second order dynamical system with asymptotically vanishing damping ⋮ Inertial primal-dual dynamics with damping and scaling for linearly constrained convex optimization problems ⋮ Fast convergence of inertial dynamics with Hessian-driven damping under geometry assumptions ⋮ First order inertial optimization algorithms with threshold effects associated with dry friction ⋮ Convergence rates of the heavy-ball method under the Łojasiewicz property ⋮ Optimal decay rates for semi-linear non-autonomous evolution equations with vanishing damping ⋮ Rate of convergence of inertial gradient dynamics with time-dependent viscous damping coefficient ⋮ Convergence Rates of Damped Inertial Dynamics under Geometric Conditions and Perturbations ⋮ An extension of the second order dynamical system that models Nesterov's convex gradient method ⋮ Optimal Convergence Rates for Nesterov Acceleration ⋮ Convergence Rates of Inertial Primal-Dual Dynamical Methods for Separable Convex Optimization Problems ⋮ Optimal energy decay rates for abstract second order evolution equations with non-autonomous damping ⋮ Convergence rates of damped inerial dynamics from multi-degree-of-freedom system

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• Asymptotics for a second-order differential equation with nonautonomous damping and an integrable source term
• Weak convergence of the sequence of successive approximations for nonexpansive mappings

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