An inertial proximal algorithm with dry friction: finite convergence results

DOI10.1007/s11228-005-0002-4zbMath1102.65063OpenAlexW2059012697MaRDI QIDQ2432517

Alexandre Cabot, Bruno Baji

Publication date: 25 October 2006

Published in: Set-Valued Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11228-005-0002-4

zbMATH Keywords

convergencemaximal monotone operatorsHilbert spacedry frictionnonlinear oscillatorproximal point algorithm

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Friction in solid mechanics (74M10) Finite difference methods applied to problems in solid mechanics (74S20) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (11)

First-order inertial algorithms involving dry friction damping ⋮ Accelerated dynamics with dry friction via time scaling and averaging of doubly nonlinear evolution equations ⋮ Unnamed Item ⋮ Digital implementation of sliding‐mode control via the implicit method: A tutorial ⋮ Asymptotics for some proximal-like method involving inertia and memory aspects ⋮ Finite Convergence of Proximal-Gradient Inertial Algorithms Combining Dry Friction with Hessian-Driven Damping ⋮ Symmetric, explicit numerical integrator for molecular dynamics equations of motion with a generalized friction ⋮ Set-Valued Sliding-Mode Control of Uncertain Linear Systems: Continuous and Discrete-Time Analysis ⋮ Asymptotics for some nonlinear damped wave equation: finite time convergence versus exponential decay results ⋮ Implicit Euler numerical scheme and chattering-free implementation of sliding mode systems ⋮ Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability

Cites Work

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• A stability theory for second-order nonsmooth dynamical systems with application to friction problems.
• Monotone Operators and the Proximal Point Algorithm
• Variational Analysis
• On the Minimizing Property of a Second Order Dissipative System in Hilbert Spaces
• Stabilization of oscillators subject to dry friction: Finite time convergence versus exponential decay results
• An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping

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