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Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings

 

作者:

 

期刊: Numerical Functional Analysis and Optimization  （Taylor Available online 1998）
卷期: Volume 19, issue 1-2  

页码: 33-56

 

ISSN:0163-0563

 

年代: 1998

 

DOI:10.1080/01630569808816813

 

出版商: Marcel Dakker Inc.,

 

关键词: 1991 Mathematics Subject Classification 47H09;1991 Mathematics Subject Classification 47H10;1991 Mathematics Subject Classification 49M45;1991 Mathematics Subject Classification 65K05;1991 Mathematics Subject Classification 65K10;1991 Mathematics Subject

 

数据来源: Taylor

 

摘要:

Letbe nonexpansive mappings on a Hilbert space H, and letbe a function which has a uniformly strongly positive and uniformly bounded second (Fréchet) derivative over the convex hull of Ti(H) for some i. We first prove that Θ has a unique minimum over the intersection of the fixed point sets of all the Ti’s at some point u*. Then a cyclic hybrid steepest descent algorithm is proposed and we prove that it converges to u*. This generalizes some recent results of Wittmann (1992), Combettes (1995), Bauschke (1996), and Yamada, Ogura, Yamashita, and Sakaniwa (1997).

 

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