多集分裂可行性问题的修正惯性投影算法  

MODIFIED INERTIAL PROJECTION ALGORITHM FOR MULTIPLE-SETS SPLIT FEASIBILITY PROBLEMS

作　　者：张冬梅 叶明露[1] Zhang Dongmei;Ye Minglu(Sichuan Colleges and Universities Key Laboratory of Optimization Theory and Applications,School of Mathematics and Information,China West Normal University,Nanchong,637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川高等院校优化理论与应用重点实验室,南充637002

出　　处：《计算数学》2024年第4期482-500,共19页Mathematica Numerica Sinica

基　　金：国家自然科学基金面上项目(11871059);西华师范大学培育项目(20A024)资助.

摘　　要：多集分裂可行性问题(MSSFP)是分裂可行性问题的推广,在图像重建、相位恢复等实际问题中具有广泛的应用.基于选择技巧,Yao等人[Optimization,2020,69(2):269-281]在Hilbert空间中提出了两种求解MSSFP的投影算法(SPA).本文修正了SPA的步长参数,提出了两种求解MSSFP的修正惯性投影算法(MISPA).在解集非空的假设条件下分别得到了MISPA的弱、强收敛性.数值实验表明:MISPA是可行的,惯性方法可以加速SPA.The Multiple-sets Split Feasibility Problem(MSSFP)is an extension of the Split Feasibility Problem and found applications in many practical problems,such as,image reconstruction and phase recovery.Based on selection techniques,Yao et al.[Optimization,2020,69(2):269-281]proposed two projection algorithms(SPA)for solving MSSFP in Hilbert space.In this paper,we modify the step-size parameter of SPA and present two modified inertial projection algorithms(MISPA)for solving MSSFP.The weak and strong convergence of MISPA are established,respectively,whenever the solution set of MSSFP is nonempty.Numerical experiments are used to show the feasibility of MISPA.Moreover,inertial technique can be used to accelerate SPA.

关 键 词：多集分裂可行性问题 选择技术 投影法 惯性方法 

分 类 号：O177[理学—数学]