Three remarks on the convergence of some discretized second order gradient-like systems

DOI10.1007/s00030-024-00974-zzbMath1543.65093MaRDI QIDQ6565519

Mohamed Ali Jendoubi, Morgan Pierre

Publication date: 2 July 2024

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

zbMATH Keywords

stabilityvariable time-step discretizationexplicit schemedescent methodsreal analytic functionsLojasiewicz gradient inequalitysingle limit-point convergence

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Numerical optimization and variational techniques (65K10)

Cites Work

• Unnamed Item
• An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions
• Convergence of global and bounded solutions of a second order gradient like system with nonlinear dissipation and analytic nonlinearity
• Convergence of solutions to second-order gradient-like systems with analytic nonlinearities
• Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
• Convergence to equilibrium of solutions of the backward Euler scheme for asymptotically autonomous second-order gradient-like systems
• On damped second-order gradient systems
• Asymptotics for some discretizations of dynamical systems, application to second order systems with non-local nonlinearities
• Convergence to equilibrium for discretized gradient-like systems with analytic features
• iPiano: Inertial Proximal Algorithm for Nonconvex Optimization
• The Convergence Problem for Dissipative Autonomous Systems
• Asymptotics for some nonlinear O.D.E. of the second order
• Non-stabilizing solutions of semilinear hyperbolic and elliptic equations with damping
• On the Minimizing Property of a Second Order Dissipative System in Hilbert Spaces
• 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
• Explicit bounds for the Łojasiewicz exponent in the gradient inequality for polynomials
• Convergence of the Iterates of Descent Methods for Analytic Cost Functions
• Fast optimization via inertial dynamics with closed-loop damping

This page was built for publication: Three remarks on the convergence of some discretized second order gradient-like systems