Damped inertial dynamics with vanishing Tikhonov regularization: strong asymptotic convergence towards the minimum norm solution

DOI10.1016/j.jde.2021.12.005zbMath1489.37113arXiv2108.00203OpenAlexW3191545112MaRDI QIDQ2069167

Hassan Riahi, Zaki Chbani, Hedy Attouch, Aicha Balhag

Publication date: 20 January 2022

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.00203

zbMATH Keywords

convex optimizationhierarchical minimizationaccelerated gradient methodsdamped inertial dynamicsNesterov accelerated gradient methodTikhonov approximation

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Convex programming (90C25) Numerical optimization and variational techniques (65K10) Management decision making, including multiple objectives (90B50) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Dynamical systems in optimization and economics (37N40)

Related Items

On the strong convergence of the trajectories of a Tikhonov regularized second order dynamical system with asymptotically vanishing damping ⋮ On the strong convergence of continuous Newton-like inertial dynamics with Tikhonov regularization for monotone inclusions ⋮ Strong Convergence of Trajectories via Inertial Dynamics Combining Hessian-Driven Damping and Tikhonov Regularization for General Convex Minimizations ⋮ A fast continuous time approach for non-smooth convex optimization using Tikhonov regularization technique ⋮ The heavy ball method regularized by Tikhonov term. Simultaneous convergence of values and trajectories ⋮ Accelerated gradient methods combining Tikhonov regularization with geometric damping driven by the Hessian

Cites Work

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• Fast convex optimization via inertial dynamics with Hessian driven damping
• On the convergence of the iterates of the ``fast iterative shrinkage/thresholding algorithm
• Inertial gradient-like dynamical system controlled by a stabilizing term
• On an asymptotically autonomous system with Tikhonov type regularizing term
• A strongly convergent primal-dual method for nonoverlapping domain decomposition
• Asymptotic behavior of gradient-like dynamical systems involving inertia and multiscale aspects
• Forward-backward and Tseng's type penalty schemes for monotone inclusion problems
• Asymptotic selection of viscosity equilibria of semilinear evolution equations by the introduction of a slowly vanishing term
• Strong asymptotic convergence of evolution equations governed by maximal monotone operators with Tikhonov regularization
• Coupling the proximal point algorithm with approximation methods
• Introductory lectures on convex optimization. A basic course.
• Asymptotic control and stabilization of nonlinear oscillators with non-isolated equilibria
• Asymptotic stabilization of inertial gradient dynamics with time-dependent viscosity
• A dynamical approach to convex minimization coupling approximation with the steepest descent method
• Asymptotic for a second order evolution equation with damping and regularizing terms
• Tikhonov regularization of a second order dynamical system with Hessian driven damping
• Asymptotic behavior of coupled dynamical systems with multiscale aspects
• Combining fast inertial dynamics for convex optimization with Tikhonov regularization
• Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity
• The Rate of Convergence of Nesterov's Accelerated Forward-Backward Method is Actually Faster Than $1/k^2$
• A Liapunov function approach to the stabilization of second order coupled systems
• Prox-Penalization and Splitting Methods for Constrained Variational Problems
• A Parallel Splitting Method for Coupled Monotone Inclusions
• Coupling Forward-Backward with Penalty Schemes and Parallel Splitting for Constrained Variational Inequalities
• On the long time behavior of second order differential equations with asymptotically small dissipation
• Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria
• The Differential Inclusion Modeling FISTA Algorithm and Optimality of Convergence Rate in the Case b $\leq3$
• Viscosity Solutions of Minimization Problems
• Proximal Point Algorithm Controlled by a Slowly Vanishing Term: Applications to Hierarchical Minimization
• Some methods of speeding up the convergence of iteration methods
• Convex analysis and monotone operator theory in Hilbert spaces
• A convergence result for nonautonomous subgradient evolution equations and its application to the steepest descent exponential penalty trajectory in linear programming