An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem
An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem
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DOI：
10.1155/2014/620813
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发表时间：
2014-03
影响因子：
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通讯作者：
Luoyi Shi;Rudong Chen;Yu Jing Wu
中科院分区：
文献类型：
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作者：
Luoyi Shi;Rudong Chen;Yu Jing Wu
多集分裂等式问题（MSSEP）要求找到一个点，使得，其中，和分别是Hilbert空间的闭凸子集，和，是两个有界线性算子.当，MSSEP被称为分裂相等问题（SEP）。如果，则MSSEP和SEP分别归结为著名的多集分裂可行性问题（MSSFP）和分裂可行性问题（SFP）。本文的目的之一是在无限维Hilbert空间的框架下，在对迭代系数较温和的条件下，给出求解SEP和MSSEP的迭代算法。
The multiple-sets split equality problem (MSSEP) requires finding a point , such that , where and are positive integers, and are closed convex subsets of Hilbert spaces , , respectively, and , are two bounded linear operators. When , the MSSEP is called the split equality problem (SEP). If , then the MSSEP and SEP reduce to the well-known multiple-sets split feasibility problem (MSSFP) and split feasibility problem (SFP), respectively. One of the purposes of this paper is to introduce an iterative algorithm to solve the SEP and MSSEP in the framework of infinite-dimensional Hilbert spaces under some more mild conditions for the iterative coefficient.