求解单调包含问题的混合邻近点算法  

A hybrid proximal points algorithm for solving monotone inclusion problems

作　　者：段复建[1] 梁劲舟 李向利[1,2] DUAN Fujian;LIANG Jingzhou;LI Xiangli(School of Mathematics&Computing Science,Guilin University of Electronic Technology,Guilin 541001,China;Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation,Guilin 541001,China;Center for Applied Mathematics of Guangxi(GUET),Guilin 541001,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541001 [2]广西高校数据分析与计算重点实验室,广西桂林541001 [3]广西应用数学中心,广西桂林541001

出　　处：《纯粹数学与应用数学》2024年第4期716-725,共10页Pure and Applied Mathematics

基　　金：国家自然科学基金(11961010).

摘　　要：在Hadamard空间提出求解单调包含问题的Mann-Halpern型黏性混合邻近点算法.在一定条件下,证明求解单调包含问题的Mann-Halpern型黏性混合邻近点算法产生的点列在Hadamard空间上具有强收敛性.最后在数值实验部分将Mann-Halpern型黏性混合邻近点算法用于求解线性反问题和极小化问题,表明新算法的可行性,有效性.In this paper,we propose a viscosity hybrid proximal points algorithm for solving the mono-tone inclusion problem in Hadamard space.Under mild conditions,we prove that this new algorithm has strong convergence.Finally,we also apply our results to solve the linear inverse problem and minimization problem.Numerical experiments are reported to illustrate the feasibility and efficiency of the new hybrid algorithm.

关 键 词：Hadamard空间 单调包含问题 黏性混合邻近点算法 强收敛 

分 类 号：O221.2[理学—运筹学与控制论]