[1]刘 颖,郭 科.一类求解多重集凸可行性问题的Valiant投影算法[J].西华师范大学学报(自然科学版),2019,40(01):72-75.[doi:10.16246/j.issn.1673-5072.2019.01.013]
 LIU Ying,GUO Ke.A Class of Valiant Projection Algorithms for Solving Multiple-sets Convex Feasibility Problems[J].Journal of China West Normal University(Natural Sciences),2019,40(01):72-75.[doi:10.16246/j.issn.1673-5072.2019.01.013]
点击复制

一类求解多重集凸可行性问题的Valiant投影算法

()
分享到:

《西华师范大学学报(自然科学版)》[ISSN:1673-5072/CN:51-1699/N]

卷:
40
期数:
2019年01期
页码:
72-75
栏目:
出版日期:
2019-03-20

文章信息/Info

Title:

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

作者:

刘  颖郭  科

(西华师范大学 数学与信息学院,四川 南充  637009)

Author(s):

LIU YingGUO Ke

(School of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China)

关键词:

凸可行性问题投影valiant投影乘积空间均值算子

Keywords:

convex feasibility problems projection valiant projection product space average operator

分类号:
O221
DOI:
10.16246/j.issn.1673-5072.2019.01.013
文献标志码:
A
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。

Abstract:

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.

相似文献/References:

[1]吴亚娟,刘晓锋,李明东.四川省城市经济增长水平评价研究[J].西华师范大学学报(自然科学版),2005,26(01):55.[doi:10.16246/j.issn.1673-5072.2005.01.013]
 WU Ya-juan,LIU X iao-feng,LIM ing-dong.Research of Evaluating Econom icalGrowth of Sichuan Cities[J].Journal of China West Normal University(Natural Sciences),2005,26(01):55.[doi:10.16246/j.issn.1673-5072.2005.01.013]
[2]郭科,张有才.广义循环Douglas-Rachford算法[J].西华师范大学学报(自然科学版),2018,39(04):404.[doi:10.16246/j.issn.1673-5072.2018.04.012]
 GUO Ke,ZHANG Youcai.Generalized Cyclic Douglas-Rachford Algorithm[J].Journal of China West Normal University(Natural Sciences),2018,39(01):404.[doi:10.16246/j.issn.1673-5072.2018.04.012]

备注/Memo

备注/Memo:

收稿日期:2018-07-02
基金项目: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)
作者简介:刘  颖(1995—),女,四川内江人,硕士研究生,主要从事最优化算法研究。E-mail:1546324471@qq.com
通信作者:郭  科(1989—),男,四川洪雅人,博士,讲师,主要从事优化算法研究。E-mail:keguo2014@126.com

更新日期/Last Update: 2018-12-20