多集分裂可行问题的算法探究  

Algorithmic Research on the Multi-Set Splitting Feasibility Problem

作　　者：朱亚 党亚峥[1] 马丁 薛中会 

机构地区：[1]上海理工大学管理学院,上海 [2]上海出版印刷高等专科学校,信息与智能工程系,上海

出　　处：《理论数学》2024年第3期240-251,共12页Pure Mathematics

摘　　要：多集分裂等式问题作为分裂可行性问题的重要拓展,在图像重建、语言处理、地震探测等领域具有重要应用。本文针对欧氏空间中多输出集的分裂可行性问题进行研究,并提出了一种新颖的松弛方法。与传统方法不同,我们采用了对两个半空间交点的投影方法。在理论上,我们在特定条件下证明了该方法的收敛性。通过数值模拟实验,进一步证实了本算法在实际应用中的有效性。The problem of multi-set splitting equations, an important extension of the split feasibility problem, has significant applications in fields such as image reconstruction, language processing, and seismic exploration. This paper investigates the split feasibility problem for multiple output sets in Euclidean spaces and proposes a novel relaxation method. Unlike traditional approaches, our method projects onto the intersection of two half-spaces. Theoretically, we prove the convergence of this method under certain conditions. Through numerical simulation experiments, the effectiveness of our algorithm in practical applications is further validated.

关 键 词：多集分裂可行性问题 CQ算法 投影算法 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]