Fast convex optimization via inertial dynamics combining viscous and Hessian-driven damping with time rescaling

DOI10.3934/eect.2021010zbMath1495.37066arXiv2009.07620OpenAlexW4287666062MaRDI QIDQ2119789

Hassan Riahi, Zaki Chbani, Hedy Attouch, Aicha Balhag

Publication date: 30 March 2022

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

Full work available at URL: https://arxiv.org/abs/2009.07620

zbMATH Keywords

time rescalingHessian-driven dampingNesterov accelerated gradient methoddamped inertial gradient dynamicsfast convex optimization

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Convex programming (90C25) Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Dynamical systems in optimization and economics (37N40)

Related Items (13)

Fast convergence of dynamical ADMM via time scaling of damped inertial dynamics ⋮ First-order frameworks for continuous Newton-like dynamics governed by maximally monotone operators ⋮ Convergence of iterates for first-order optimization algorithms with inertia and Hessian driven 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 ⋮ Fast continuous dynamics inside the graph of subdifferentials of nonsmooth convex functions ⋮ Strong Convergence of Trajectories via Inertial Dynamics Combining Hessian-Driven Damping and Tikhonov Regularization for General Convex Minimizations ⋮ Practical perspectives on symplectic accelerated optimization ⋮ The heavy ball method regularized by Tikhonov term. Simultaneous convergence of values and trajectories ⋮ Continuous Newton-like Methods Featuring Inertia and Variable Mass ⋮ Improved convergence rates and trajectory convergence for primal-dual dynamical systems with vanishing damping ⋮ Tikhonov Regularization of a Perturbed Heavy Ball System with Vanishing Damping ⋮ A fast continuous time approach with time scaling for nonsmooth convex optimization

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