一类求解多重集凸可行性问题的Valiant投影算法  

A Class of Valiant Projection Algorithms for Solving Multiple-sets Convex Feasibility Problems

作　　者：刘颖 郭科[1] LIU Ying;GUO Ke(School of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2019年第1期72-75,共4页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金资助项目(11571178;11801455);西华师范大学博士科研启动基金(17E084;18B031);2018年省级大学生创新创业训练计划项目(201810638047)

摘　　要：对于多重集凸可行性问题,交替投影算法是求解该问题的最常用方法之一。利用乘积空间技术,可以将多重集凸可行性问题转化为两个集合的可行性问题,从而提高算法的效率。对于闭凸集上的投影难以计算的情况,Censor最近提出了交替valiant投影算法,在每次迭代中仅需向包含该闭凸集的一个扩大的闭凸集上作投影,该算法比经典的交替投影算法更有效。本文借助valiant投影的思想和乘积空间技术,提出了一种求解多重集凸可行性问题的算法,并证明了算法的收敛性。Alternating projection algorithm is one of the most useful methods for solving the multiple-sets convex feasibility problems.To improve the efficiency of the algorithm,multiple-sets convex feasibility problems can be transformed to two sets convex feasibility problem by using the product space strategy.When the projection onto the closed convex set is hard to calculate,Bauschke recently proposed the valiant alternating projection algorithm.The projection is executed on a closed convex set containing the original set in each iteration,making the algorithm more effective than the classical alternating projection algorithm.The purpose of this paper is to propose an new algorithm for solving multiple-sets convex feasibility problems and show its convergence by using the idea of valiant projection and the strategy of product space.

关 键 词：凸可行性问题 投影 valiant投影 乘积空间 均值算子 

分 类 号：O221[理学—运筹学与控制论]