Visco-penalization of the sum of two monotone operators

被引：7

作者：

Combettes, Patrick L. ^{[1
]}

Hirstoaga, Sever A. ^{[2
]}

机构：

[1] Univ Paris 06, Fac Math, Lab Jacques Louis Lions, F-75005 Paris, France

[2] Univ Paris 09, CEREMADE, F-75775 Paris, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 69卷 / 02期

关键词：

approximating curve; monotone operator; penalization; variational inequality; viscosity; Yosida approximation;

D O I：

10.1016/j.na.2007.06.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new type of approximating curve for finding a particular zero of the sum of two maximal monotone operators in a Hilbert space is investigated. This curve consists of the zeros of perturbed problems in which one operator is replaced with its Yosida approximation and a viscosity term is added. As the perturbation vanishes, the curve is shown to converge to the zero of the sum that solves a particular strictly monotone variational inequality. As an off-spring of this result, we obtain an approximating curve for finding a particular zero of the sum of several maximal monotone operators. Applications to convex optimization are discussed. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：579 / 591

页数：13

共 26 条

[1] A NEW APPROACH TO THE INVESTIGATION OF EVOLUTION DIFFERENTIAL-EQUATIONS IN BANACH-SPACES [J].

ALBER, YI .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1994, 23 (09) :1115-1134

[2] A dynamical approach to convex minimization coupling approximation with the steepest descent method [J].

Attouch, H ;

Cominetti, R .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 128 (02) :519-540

[3]

Attouch H., 1984, Applicable Mathematics Series

[4]

Attouch H., 1994, J. Convex Analysis, V1, P1

[5]

Attouch H., 1996, J. Convex Anal., V3, P1

[6]

Attouch H., 1986, N HOLLAND MATH LIB, V34, P125

[7]

Aubin J. P., 1990, Set-valued analysis, DOI 10.1007/978-0-8176-4848-0

[8] The asymptotic behavior of the composition of two resolvents [J].

Bauschke, HH ;

Combettes, PL ;

Reich, S .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 60 (02) :283-301

[9] IMAGE OF SUM OF MONOTONE OPERATORS AND APPLICATIONS [J].

BREZIS, H ;

HARAUX, A .

ISRAEL JOURNAL OF MATHEMATICS, 1976, 23 (02) :165-186

[10] PERTURBATIONS OF NONLINEAR MAXIMAL MONOTONE SETS IN BANACH SPACE [J].

BREZIS, H ;

CRANDALL, MG ;

PAZY, A .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1970, 23 (01) :123-&

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