A second-order gradient-like dissipative dynamical system with Hessian-driven damping. Application to optimization and mechanics

Journal des Mathematiques Pures et Appliquees

Volumn 81, Issue 8, 2002, Pages 747-779

  Alvarez, F ^a   Attouch, H ^b   Bolte, J ^b   Redont, P ^b  

^a UNIVERSITY OF CHILE   (Chile)

^b CNRS   (France)

Author keywords

Asymptotic behaviour; Continuous Newton method; Dissipative dynamical systems; Gradiant project methods; Gradient like dynamical systems; Optimal control; Second order in time dynamical system; Shocks in mechanics

Indexed keywords

EID: 0036347388     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-7824(01)01253-3     Document Type: Article

References (35)

1. A new approach of strong stabilization of distributed systems
2. On the minimizing property of a second-order dissipative system in Hilbert space
3. An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping
4. A dynamical system associated with Newton's method for parametric approximations of convex minimization problems
5. Linearization method, in nonlinear dynamic systems: Qualitative analysis and control (in Russian)
6. Minimization of convex functions on convex sets by means of differential equations (in Russian)
7. Continuous second-order linearization method for convex programming problems
8. The heavy ball with friction dynamical system for convex constrained minimization problems
9. The dynamics of elastic shocks via epigraphical regularization of a differential inclusion. Barrier and penalty approximations
10. A dynamical approach to convex minimization coupling approximation with the steepest descent method
11. The heavy ball with friction method, I. The continuous dynamical system: Global exploration of the global minima of a real-valued function by asymptotic analysis of a dissipative dynamical system
12. The second-order in time continuous Newton method
13. Un exemple concernant le comportement asymptotique de la solution du problème du/dt + ∂ψ(u) ∋ 0
14. Opérateurs Maximaux Monotones
15. Asymptotic convergence of nonlinear contraction semigroups in Hilbert space
16. Asymptotic behavior of dissipative systems
17. Semilinear hyperbolic problems in bounded domains
18. Systèmes Dynamiques Dissipatifs et Applications
19. Convergence of solutions of second-order gradient-like systems with analytic nonlinearities
20. Convergence of bounded and global solutions of the wave equation with linear dissipation and analytic nonlinearity
21. Generalized Newton and NCP Methods: Convergence, regularity, actions
22. Une propriété topologique des sous-ensembles analytiques réels
23. Ensembles semi-analytiques
24. On second-order subdifferentials and their applications
25. Weak convergence of the sequence of successive approximations for nonexpansive mappings
26. Mouvement à un nombre fini de degrés de liberté avec contraintes unilatérales: Cas avec perte d'énergie
27. Ill-posedness in vibro-impact and its numerical consequences
28. Introduction to Optimization, Optimization Software
29. Asymptotics for a class of non-linear evolution equations, with applications to geometric problems
30. A convergent process of price adjustment and global Newton methods
31. Infinite dimensional dynamical systems in mechanics and physics