A proximal method for maximal monotone operators via discretization of a first order dissipative dynamical system

被引：0

作者：

Mainge, Paul-Emile ^{[1
]}

Moudafi, Abdellatif ^{[1
]}

机构：

[1] Univ Antilles Guyane, GRIMMAG, Dept Sci Interfac, F-97230 Martinique, France

来源：

JOURNAL OF CONVEX ANALYSIS | 2007年 / 14卷 / 04期

关键词：

monotone operators; standard and inertial proximal methods; minimization;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：869 / 878

页数：10

共 17 条

[1] Alvarez F, 1998, APPL MATH OPT, V38, P193
[2] On the minimizing property of a second order dissipative system in Hilbert spaces
Alvarez, F
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 38 (04) : 1102 - 1119
[3] A second-order gradient-like dissipative dynamical system with Hessian-driven damping. Application to optimization and mechanics
Alvarez, F
Attouch, H
Bolte, J
Redont, P
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2002, 81 (08): : 747 - 779
[4] An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping
Alvarez, F
Attouch, H
[J]. SET-VALUED ANALYSIS, 2001, 9 (1-2): : 3 - 11
[5] Using the banach contraction principle to implement the proximal point method for multivalued monotone variational inequalities
Anh, P
Muu, LD
Nguyen, VH
Strodiot, JJ
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2005, 124 (02) : 285 - 306
[6] 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
Attouch, H
Goudou, X
Redont, P
[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2000, 2 (01) : 1 - 34
[7] Attouch H, 2001, APPROXIMATION, OPTIMIZATION AND MATHEMATICAL ECONOMICS, P25
[8] Auslender A, 1976, Optimisation: Methodes numeques
[9] BREZIS H., 1973, North-Holland Math. Stud., V5
[10] Enlargement of monotone operators with applications to variational inequalities
Burachik, RS
Iusem, AN
Svaiter, BF
[J]. SET-VALUED ANALYSIS, 1997, 5 (02): : 159 - 180

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