Geodesic
A Proximal Method for Maximal Monotone Operators via Discretization of a First Order Dissipative Dynamical System
Journal of convex analysis, Tome 14 (2007) no. 4, pp. 869-878

Voir la notice de l'article provenant de la source Heldermann Verlag

We present an iterative method for finding zeroes of maximal monotone operators in a real Hilbert space. The underlying idea relies upon the discretization of a first order dissipative dynamical system which allows us to preserve the local feature, as well as to obtain convergence results. The main theorems do not only recover known convergence results of standard and inertial proximal methods, but also provide a theoretical basis for the application of new iterative methods.
Classification : 49J53, 65K10, 49M37, 90C25
Mots-clés : Monotone operators, standard and inertial proximal methods, minimization 
@article{JCA_2007_14_4_JCA_2007_14_4_a9,
     author = {P.-E. Maing\'e and A. Moudafi},
     title = {A {Proximal} {Method} for {Maximal} {Monotone} {Operators} via {Discretization} of a {First} {Order} {Dissipative} {Dynamical} {System}},
     journal = {Journal of convex analysis},
     pages = {869--878},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2007},
     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_4_JCA_2007_14_4_a9/}
}
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P.-E. Maingé; A. Moudafi. A Proximal Method for Maximal Monotone Operators via Discretization of a First Order Dissipative Dynamical System. Journal of convex analysis, Tome 14 (2007) no. 4, pp. 869-878. http://geodesic.mathdoc.fr/item/JCA_2007_14_4_JCA_2007_14_4_a9/