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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (2): 298-306.doi: 10.3969/j.issn.1005-3085.2015.02.014

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分裂可行问题的两种强收敛CQ算法(英)

党亚峥1,   薛中会2,   高   岩1   

  1. 1- 上海理工大学管理学院，上海 200093
    2- 河南理工大学理化学院，焦作 454001
  • 收稿日期:2013-07-14 接受日期:2014-09-01 出版日期:2015-04-15 发布日期:2015-06-15
  • 基金资助:
    国家自然科学基金 (11171221; 61403255)；中国高等学校博士点基金 (20123120110004)；中国煤炭工业协会2011年度科技指导计划 (MTKJ-2011-404)；上海市自然科学基金 (14ZR1429200)；上海市重点学科建设项目 (XTKX2012)；上海市教委创新计划 (15ZZ073)；上海理工大学博士点项目 (ID-10-303-002)；上海市科技青年教师培训项目.

Two Strongly Convergent CQ Algorithms for Split Feasibility Problem

DANG Ya-zheng1,   XUE Zhong-hui2,   GAO Yan1   

  1. 1- School of Management, University of Shanghai for Science and Technology, Shanghai 200093
    2- School of Physics and Chemistry, Henan Polytechnic University, Jiaozuo 454001
  • Received:2013-07-14 Accepted:2014-09-01 Online:2015-04-15 Published:2015-06-15
  • Supported by:
    The National Natural Science Foundation of China (11171221; 61403255); the Doctoral Program Foundation of Institutions of Higher Education of China (20123120110004); the China Coal Industry Association 2011 Annual Scientific and Technical Guidance Programs (MTKJ-2011-404); the Natural Science Foundation of Shanghai (14ZR1429200); the Shanghai Leading Academic Discipline Project (XTKX2012); the Innovation Program of Shanghai Municipal Education Commission (15ZZ073); the Doctoral Starting Projection of the University of Shanghai for Science and Technology (ID-10-303-002); the Young Teacher Training Projection Program of Shanghai for Science and Technology. 

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摘要： 为保证Hilbert空间中求解分裂可行问题迭代算法的强收敛性，本文首先通过引入三个参数序列提出了求解分裂可行问题的改进CQ算法，并在较弱的条件下证明了算法的强收敛性．然后改进算法中的一个算子，即选择另外一个参数序列嵌入到一个算子里，得到了一种新的算法．在参数序列满足一定条件下也证明了算法的强收敛性．本文拓展了现已有的相关研究成果．

关键词: 分裂可行问题, 改进CQ算法, 强收敛性

Abstract:

In thins paper, in order to ensure the strong convergence of the iterative procedure for solving split feasibility problem in a real Hilbert space. We firstly construct a modified CQ algorithm by introducing three parametric sequences and prove its strong convergence under some weak conditions. Furthermore, we put another parametric sequence in one operator in the presented algorithm to get a new algorithm, and also prove its strong convergence under some conditions on the parametric sequence. The results in this paper improve and extend the corresponding results.

Key words: split feasibility problem, modified CQ algorithm, strong convergence

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