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Hilbert空间中求解分裂可行问题CQ算法的强收敛性

 引用本文: 赵世莲. Hilbert空间中求解分裂可行问题CQ算法的强收敛性[J]. 应用数学和力学, 2019, 40(1): 108-114.
ZHAO Shilian. Strong Convergence of CQ Algorithms for Split Feasibility Problems in the Hilbert Spaces[J]. Applied Mathematics and Mechanics, 2019, 40(1): 108-114. doi: 10.21656/1000-0887.390012
 Citation: ZHAO Shilian. Strong Convergence of CQ Algorithms for Split Feasibility Problems in the Hilbert Spaces[J]. Applied Mathematics and Mechanics, 2019, 40(1): 108-114.

## Hilbert空间中求解分裂可行问题CQ算法的强收敛性

##### doi: 10.21656/1000-0887.390012

###### 作者简介:赵世莲（1984—），女，讲师，硕士(E-mail: 14622959@qq.com).
• 中图分类号: O177.91

## Strong Convergence of CQ Algorithms for Split Feasibility Problems in the Hilbert Spaces

Funds: The National Natural Science Foundation of China（11371015）
• 摘要: 在Hilbert空间中,为了研究分裂可行问题迭代算法的强收敛性,提出了一种新的CQ算法.首先利用CQ算法构造了一个改进的Halpern迭代序列； 然后通过把分裂可行问题转化为算子不动点， 在较弱的条件下， 证明了该序列强收敛到分裂可行问题的一个解. 推广了Wang和Xu的有关结果.
•  [1] BYRNE C. A unified treatment of some iterative algorithms in signal processing and image reconstruction[J]. Inverse Problems,2004,20(1): 103-120. [2] CENSOR Y, ELFVING T, KOPF N, et al. The multiple-sets split feasibility problem and its applications for inverse problems[J]. Inverse Problems,2005,21(6): 2017-2084. [3] CENSOR Y, BORTFELD T, MARTIN B, et al. A unified approach for inversion problems intensity-modulated radiation therapy[J]. Physics in Medicine and Biology,2006,51(10): 2353-2365. [4] CENSOR Y, MOTOVA A, SEGAL A. Perturbed projections and subgradient projections for the multiple-sets split feasibility problem[J]. Journal of Mathematical Analysis and Applications,2007,327(2): 1244-1256. [5] CENSOR Y, ELFVING T. A multiprojection algorithm using Bregman projections in a product space[J]. Numerical Algorithms,1994,8(2): 221-239. [6] YANG Q Z. The relaxed CQ algorithm solving the split feasibility problem[J]. Inverse Problems,2004,20(4): 1261-1266. [7] QU B, XIU N H. A note on the CQ algorithm for the split feasibility problem[J]. Inverse Problems,2005,21(5): 1655-1665. [8] DANG Y Z,GAO Y. The strong convergence of a KM-CQ-like algorithm for split feasibility problem[J]. Inverse Problems,2011,27(1): 1-9. [9] 杨丽, 李军. Hilbert空间中分裂可行性问题的改进Halpern 迭代和黏性逼近算法[J]. 应用数学和力学, 2017,38(9): 1072-1080.(YANG Li, LI Jun. Modified Halpern iteration and viscosity approximation methods for split feasibility problems in Hilbert spaces[J]. Applied Mathematics and Mechanics,2017,38(9): 1072-1080.(in Chinese)) [10] BYRNE C. Iterative oblique projection onto convex sets and the split feasibility problem[J]. Inverse Problems,2002,18(2): 441-453. [11] XU H K. Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces[J]. Inverse Problems,2010,26(10): 1-17. [12] XU H K. A variable Krasnosel’skii-Mann algorithm and the multiple-set split feasibility problem[J]. Inverse Problems,2006,22(6): 2021-2034. [13] WANG F H, XU H K. Approximating curve and strong convergence of the CQ algorithm for the split feasibility problem[J]. Journal of Inequalities and Application,2010,2010(1): 1-13. [14] GOEBEL K, KIRK W A. Topics in Metric Fixed Point Theory [M]. Cambridge: Cambridge University Press, 1990. [15] XU H K. Viscosity approximation methods for nonexpansive mappings[J]. Journal of Mathematical Analysis and Applications,2004,298(1): 279-291.
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##### 出版历程
• 收稿日期:  2018-01-08
• 修回日期:  2018-03-26
• 刊出日期:  2019-01-01

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