Relaxed extragradient methods for finding minimum-norm solutions of the split feasibility problem

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• 作者：L.-C. Ceng^a ; ^{zenglc@hotmail.com} ; Q.H. Ansari^b ; ^{qhansari@gmail.com} ; J.-C. Yao^c ; ^{yaojc@cc.kmu.edu.tw}
• 关键词：47H10 ; 65J20 ; 65J22 ; 65J25
• 刊名：Nonlinear Analysis
• 出版年：2012
• 出版时间：March 2012
• 年：2012
• 卷：75
• 期：4
• 页码：2116-2125
• 全文大小：243 K

文摘

In this paper, we consider the split feasibility problem (SFP) in infinite-dimensional Hilbert spaces, and study the relaxed extragradient methods for finding a common element of the solution set of SFP and the set of fixed points of a nonexpansive mapping . Combining Mann¡¯s iterative method and Korpelevich¡¯s extragradient method, we propose two iterative algorithms for finding an element of . On one hand, for , the identity mapping, we derive the strong convergence of one iterative algorithm to the minimum-norm solution of the SFP under appropriate conditions. On the other hand, we also derive the weak convergence of another iterative algorithm to an element of under mild assumptions.