NEW ITERATIVE REGULARIZATION METHODS FOR SOLVING SPLIT VARIATIONAL INCLUSION PROBLEMS

被引：0

作者：

Dang Van Hieu ^{[1
]}

Le Dung Muu ^{[2
]}

Pham Kim Quy ^{[3
]}

机构：

[1] TIMAS Thang Long Univ, Hanoi, Vietnam

[2] VAST, Inst Math, 18 Hoang Quoc Viet, Hanoi, Vietnam

[3] Coll Air Force, Dept Basic Sci, Nha Trang City, Vietnam

来源：

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION | 2023年 / 19卷 / 01期

关键词：

Split variational inclusion; split feasibility problem; regularization method; iterative method; FEASIBILITY PROBLEMS; COMMON SOLUTIONS; ALGORITHMS; PROJECTION; SETS;

D O I：

10.3934/jimo.2021185

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The paper proposes some new iterative algorithms for solving a split variational inclusion problem involving maximally monotone multi-valued operators in a Hilbert space. The algorithms are constructed around the resolvent of operator and the regularization technique to get the strong convergence. Some stepsize rules are incorporated to allow the algorithms to work easily. An application of the proposed algorithms to split feasibility problems is also studied. The computational performance of the new algorithms in comparison with others is shown by some numerical experiments.

引用

页码：300 / 320

页数：21

共 35 条

[1]

Brezis H., 1973, N HOLLAND MATH STUD, V5, P19, DOI DOI 10.1016/S0304-0208(08)72383-1

[2] Iterative oblique projection onto convex sets and the split feasibility problem [J].

Byrne, C .

INVERSE PROBLEMS, 2002, 18 (02) :441-453

[3] A unified treatment of some iterative algorithms in signal processing and image reconstruction [J].

Byrne, C .

INVERSE PROBLEMS, 2004, 20 (01) :103-120

[4]

Byrne C, 2012, J NONLINEAR CONVEX A, V13, P759

[5] The multiple-sets split feasibility problem and its applications for inverse problems [J].

Censor, Y ;

Elfving, T ;

Kopf, N ;

Bortfeld, T .

INVERSE PROBLEMS, 2005, 21 (06) :2071-2084

[6]

Censor Y., 1994, Numer. Algorithms, V8, P221, DOI [DOI 10.1007/BF02142692, 10.1007/BF02142692]

[7] A von Neumann alternating method for finding common solutions to variational inequalities [J].

Censor, Yair ;

Gibali, Aviv ;

Reich, Simeon .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (12) :4596-4603

[8] Common Solutions to Variational Inequalities [J].

Censor, Yair ;

Gibali, Aviv ;

Reich, Simeon ;

Sabach, Shoham .

SET-VALUED AND VARIATIONAL ANALYSIS, 2012, 20 (02) :229-247

[9] Algorithms for the Split Variational Inequality Problem [J].

Censor, Yair ;

Gibali, Aviv ;

Reich, Simeon .

NUMERICAL ALGORITHMS, 2012, 59 (02) :301-323

[10]

Censor Y, 2008, CRM SER, V7, P65

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