The steepest descent dynamical system with control. Applications to constrained minimization

DOI10.1051/cocv:2004005zbMath1072.49004OpenAlexW2037498722MaRDI QIDQ5465549

Alexandre Cabot

Publication date: 9 August 2005

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=COCV_2004__10_2_243_0

zbMATH Keywords

constrained optimizationasymptotic behaviourconvex minimizationsteepest descent methoddissipative dynamical systemnon-linear oscillator

Mathematics Subject Classification ID

Related Items (12)

Asymptotic for a second order evolution equation with damping and regularizing terms ⋮ Dynamical systems and forward–backward algorithms associated with the sum of a convex subdifferential and a monotone cocoercive operator ⋮ Asymptotic behavior of coupled dynamical systems with multiscale aspects ⋮ Global Dynamical Solvers for Nonlinear Programming Problems ⋮ Existence, stability and optimality for optimal control problems governed by maximal monotone operators ⋮ Feedback stabilization methods for the solution of nonlinear programming problems ⋮ A coupled problem described by time-dependent subdifferential operator and non-convex perturbed sweeping process ⋮ Iterative regularization via dual diagonal descent ⋮ Evolution differential inclusion with projection for solving constrained nonsmooth convex optimization in Hilbert space ⋮ Strong asymptotic convergence of evolution equations governed by maximal monotone operators with Tikhonov regularization ⋮ Asymptotic behavior of gradient-like dynamical systems involving inertia and multiscale aspects ⋮ Asymptotic behavior analysis on multivalued evolution inclusion with projection in Hilbert space

Cites Work

• Stability by Liapunov's direct method. With applications
• Asymptotic convergence of nonlinear contraction semigroups in Hilbert space
• Asymptotic control and stabilization of nonlinear oscillators with non-isolated equilibria
• A dynamical approach to convex minimization coupling approximation with the steepest descent method
• 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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