HYBRID EXTRAGRADIENT METHODS FOR FINDING MINIMUM-NORM SOLUTIONS OF SPLIT FEASIBILITY PROBLEMS

被引：0
|
作者：
Ceng, Lu-Chuan [2 ,3 ]
Wong, Ngai-Ching [1 ,4 ]
Yao, Jen-Chih [5 ]
机构：
[1] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan
[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
[3] Sci Comp Key Lab Shanghai Univ, Shanghai 200234, Peoples R China
[4] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan
[5] China Med Univ, Ctr Gen Educ, Taichung 40402, Taiwan
来源：
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2015年 / 16卷 / 10期
基金：
美国国家科学基金会;
关键词：
Split feasibility problems; fixed point problems; hybrid extragradient methods; strictly pseudocontractive mappings; nonexpansive mappings; minimum-norm solutions; demiclosedness principle; algorithms; FIXED-POINT PROBLEMS; VARIATIONAL-INEQUALITIES; NONEXPANSIVE-MAPPINGS; STRONG-CONVERGENCE; MONOTONE MAPPINGS; WEAK-CONVERGENCE; PROJECTION METHODS; HILBERT-SPACES; CQ ALGORITHM; SETS;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the split feasibility problem (SFP) on a nonempty closed convex subset C of a Hilbert space of arbitrary dimension. When C is given as the common fixed point set of nonexpansive mappings, combining Mann's iterative method, Korpelevich's extragradient method and the hybrid steepest-descent method, we develop an iterative algorithm. This algorithm provides the strong convergence to the minimum-norm solution of the SFP. On the other hand, we study the hybrid extragradient methods for finding a common element of the solution set Gamma of the SFP and the set Fix(S) of fixed points of a strictly pseudocontractive mapping S. We propose an iterative algorithm which generates sequences converging weakly to an element of Fix(S) boolean AND Gamma.
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页码：1965 / 1983
页数：19
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