Banach空间中有限个极大单调算子公共零点的迭代格式

魏利; 周海云

doi:10.12341/jssms08765

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系统科学与数学 ›› 2007, Vol. 27 ›› Issue (2) : 184-193. DOI: 10.12341/jssms08765

论文

Banach空间中有限个极大单调算子公共零点的迭代格式

魏利(1), 周海云(2)

作者信息 +

Iterative Scheme of Common Zero Points for Finite Maximal Monotone Operators in Banach Space

Wei Li(1), Zhou Haiyun(2)

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文章历史 +

摘要

令E为实光滑、一致凸Banach空间, E* 为其对偶空间.令A_i,B_i \subset E × E*, i = 1,2,...,m,
为极大单调算子且∪^m_i=1(A_i^-10∪B_i^-10)≠emptyset. 引入新的迭代算法,并利用Lyapunov泛函,Q_r算子与广义投影算子等技巧,证明迭代序列弱收敛于极大单调算子A_i,B_i,i =1,2,...,m的公共零点的结论.

Abstract

Let

E

be a real smooth and uniformly convex space with

E^{*}

its duality space. For

i = 1, 2, \dots, m,

let

A_{i}, B_{i} \subset E \times E^{*}

be maximal monotone operators with

⋂_{i = 1}^{m} (A_{i}^{- 1} 0 ⋂ B_{i}^{- 1} 0) \neq \emptyset

. A new iterative scheme is introduced which is proved to be weakly convergent to common zero points of maximal monotone operators

A_{i}

and

B_{i}, i = 1, 2, \dots, m

by using the techniques of Lyapunov functionals,

Q_{r}

operators, and generalized projection operators, etc.

导出引用

魏利 , 周海云. Banach空间中有限个极大单调算子公共零点的迭代格式. 系统科学与数学, 2007, 27(2): 184-193. https://doi.org/10.12341/jssms08765

Wei Li , Zhou Haiyun. Iterative Scheme of Common Zero Points for Finite Maximal Monotone Operators in Banach Space. Journal of Systems Science and Mathematical Sciences, 2007, 27(2): 184-193 https://doi.org/10.12341/jssms08765

中图分类号： 47H05 47H09

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收稿日期	修回日期	出版日期
1900-01-01	1900-01-01	2007-04-25
发布日期
2007-04-25

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