Inertial gradient-like dynamical system controlled by a stabilizing term

DOI10.1023/B:JOTA.0000015685.21638.8dzbMath1070.90107OpenAlexW2044475762MaRDI QIDQ597147

Sumit K. Garg

Publication date: 6 August 2004

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/b:jota.0000015685.21638.8d

zbMATH Keywords

optimizationnonlinear oscillatorsconvex minimizationDissipative dynamical systemsheavy ball with friction

Mathematics Subject Classification ID

Nonlinear programming (90C30) Control of mechanical systems (70Q05) Problems involving a system of particles with friction (70F40) Dynamical systems in control (37N35)

Related Items (9)

Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects ⋮ Strong Convergence of Trajectories via Inertial Dynamics Combining Hessian-Driven Damping and Tikhonov Regularization for General Convex Minimizations ⋮ Accelerated gradient methods combining Tikhonov regularization with geometric damping driven by the Hessian ⋮ Evolution differential inclusion with projection for solving constrained nonsmooth convex optimization in Hilbert space ⋮ Asymptotic behavior of gradient-like dynamical systems involving inertia and multiscale aspects ⋮ On the long time behavior of second order differential equations with asymptotically small dissipation ⋮ Damped inertial dynamics with vanishing Tikhonov regularization: strong asymptotic convergence towards the minimum norm solution ⋮ Asymptotic behavior analysis on multivalued evolution inclusion with projection in Hilbert space ⋮ Asymptotic control and stabilization of nonlinear oscillators with non isolated equilibria, a note: from \(L^1\) to non \(L^1\)

Cites Work

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• THE HEAVY BALL WITH FRICTION METHOD, I. THE CONTINUOUS DYNAMICAL SYSTEM: GLOBAL EXPLORATION OF THE LOCAL MINIMA OF A REAL-VALUED FUNCTION BY ASYMPTOTIC ANALYSIS OF A DISSIPATIVE DYNAMICAL SYSTEM
• Asymptotic Control of Pairs of Oscillators Coupled by a Repulsion, with Nonisolated Equilibria I: The Regular Case
• Weak convergence of the sequence of successive approximations for nonexpansive mappings

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