Strong convergence of a self-adaptive method for the split feasibility problem

被引：122

作者：

Yao, Yonghong ^{[1
]}

Postolache, Mihai ^{[2
]}

Liou, Yeong-Cheng ^{[3
]}

机构：

[1] Tianjin Polytech Univ, Dept Math, Tianjin 300387, Peoples R China

[2] Univ Politehn Bucuresti, Fac Sci Appl, Bucharest 060042, Romania

[3] Cheng Shiu Univ, Dept Informat Management, Kaohsiung 833, Taiwan

来源：

FIXED POINT THEORY AND APPLICATIONS | 2013年

关键词：

split feasibility problem; self-adaptive method; projection; minimization problem; minimum-norm; VARIATIONAL INEQUALITY PROBLEMS; POLYAK PROJECTION METHOD; FIXED-POINT PROBLEMS; ITERATIVE ALGORITHMS; CONVEX MINIMIZATION; OPERATORS; SETS;

D O I：

10.1186/1687-1812-2013-201

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Self-adaptive methods which permit step-sizes being selected self-adaptively are effective methods for solving some important problems, e. g., variational inequality problems. We devote this paper to developing and improving the self-adaptive methods for solving the split feasibility problem. A new improved self-adaptive method is introduced for solving the split feasibility problem. As a special case, the minimum norm solution of the split feasibility problem can be approached iteratively.

引用

页数：12

共 49 条

[1] Projection algorithms for solving convex feasibility problems [J].

Bauschke, HH ;

Borwein, JM .

SIAM REVIEW, 1996, 38 (03) :367-426

[2]

Bregman L. M., 1967, USSR Comput Math Math Phys, V7, P200, DOI [10.1016/0041-5553(67)90040-7, DOI 10.1016/0041-5553(67)90040-7]

[3] ON THE BEHAVIOR OF A BLOCK-ITERATIVE PROJECTION METHOD FOR SOLVING CONVEX FEASIBILITY PROBLEMS [J].

BUTNARIU, D ;

CENSOR, Y .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1990, 34 (1-2) :79-94

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

Byrne, C .

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

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

Byrne, C .

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

[6]

Byrne Charles., 2001, Studies in Computational Mathematics, V8, P87

[7] Relaxed extragradient methods for finding minimum-norm solutions of the split feasibility problem [J].

Ceng, L. -C. ;

Ansari, Q. H. ;

Yao, J. -C. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (04) :2116-2125

[8] Some iterative methods for finding fixed points and for solving constrained convex minimization problems [J].

Ceng, L. -C. ;

Ansari, Q. H. ;

Yao, J. -C. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (16) :5286-5302

[9] An extragradient method for solving split feasibility and fixed point problems [J].

Ceng, L-C ;

Ansari, Q. H. ;

Yao, J-C .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 64 (04) :633-642

[10] EXTRAGRADIENT-PROJECTION METHOD FOR SOLVING CONSTRAINED CONVEX MINIMIZATION PROBLEMS [J].

Ceng, Lu-Chuan ;

Ansari, Qamrul Hasan ;

Yao, Jen-Chih .

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION, 2011, 1 (03) :341-359

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