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数值计算与计算机应用  2018, Vol. 39 Issue (1): 20-27    DOI:
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求解结构型分裂可行问题的一种交替方向法
孙聿童, 赵金玲
北京科技大学数理学院, 北京 100083
AN ALTERNATING DIRECTIONS METHOD FOR STRUCTURED SPLIT FEASIBILITY PROBLEMS
Sun Yutong, Zhao Jinling
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
 全文: PDF (345 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料
摘要 基于结构型分裂可行问题的分离性结构,考虑用交替方向法来求解结构型分裂可行问题.并且给出算法的收敛性说明.提出的新算法不需要在每次迭代过程中计算向集合C的投影,并且可以将高维度的问题转化为低维度的问题.另外初步的数值实验结果表明用此方法是可行且高效的,尤其在时间方面大大的提高了计算效率.
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关键词结构型分裂可行问题   交替方向法   单调   投影     
Abstract: Recently, the alternating directions method has attracted great attention. In this paper we apply alternating directions method for solving structured split feasibility problems. We first reduce the structured split feasibility problem into two smaller scale sub-problems, and then employ alternating directions method to solve them. By this method, instead of computing projection onto the convex set C in every iteration, we only need to compute projections onto simple sets X and Y, which greatly reduces the computational time. The convergence of this method is valid under mild assumptions and its efficiency is also verified by some numerical experiments.
Key wordsstructured split feasibility problem   alternating directions method   monotone   projection   
收稿日期: 2016-10-08;
基金资助:

国家自然科学基金青年基金项目资助(11101028),北京高校青年英才计划资助(YETP0385).

引用本文:   
. 求解结构型分裂可行问题的一种交替方向法[J]. 数值计算与计算机应用, 2018, 39(1): 20-27.
. AN ALTERNATING DIRECTIONS METHOD FOR STRUCTURED SPLIT FEASIBILITY PROBLEMS[J]. Journal of Numerical Methods and Computer Applicat, 2018, 39(1): 20-27.
 
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