Accelerated Mann and CQ algorithms for finding a fixed point of a nonexpansive mapping

doi:10.1186/s13663-015-0374-6

CSpace

	Accelerated Mann and CQ algorithms for finding a fixed point of a nonexpansive mapping
	Dong,Qiao-Li 1,2; Yuan,Han-bo 1
	2015-07-22
发表期刊	Fixed Point Theory and Applications
ISSN	1687-1812
卷号	2015 期号:1
摘要	AbstractThe purpose of this paper is to present accelerations of the Mann and CQ algorithms. We first apply the Picard algorithm to the smooth convex minimization problem and point out that the Picard algorithm is the steepest descent method for solving the minimization problem. Next, we provide the accelerated Picard algorithm by using the ideas of conjugate gradient methods that accelerate the steepest descent method. Then, based on the accelerated Picard algorithm, we present accelerations of the Mann and CQ algorithms. Under certain assumptions, we show that the new algorithms converge to a fixed point of a nonexpansive mapping. Finally, we show the efficiency of the accelerated Mann algorithm by numerically comparing with the Mann algorithm. A numerical example is provided to illustrate that the acceleration of the CQ algorithm is ineffective.
关键词	nonexpansive mapping convex minimization problem Picard algorithm Mann algorithm CQ algorithm conjugate gradient method steepest descent method
DOI	10.1186/s13663-015-0374-6
语种	英语
WOS记录号	BMC:10.1186/s13663-015-0374-6
出版者	Springer International Publishing
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/339
专题	中国科学院数学与系统科学研究院
通讯作者	Dong,Qiao-Li
作者单位	1.Civil Aviation University of China; College of Science 2.Civil Aviation University of China; Tianjin Key Lab for Advanced Signal Processing
推荐引用方式 GB/T 7714	Dong,Qiao-Li,Yuan,Han-bo. Accelerated Mann and CQ algorithms for finding a fixed point of a nonexpansive mapping[J]. Fixed Point Theory and Applications,2015,2015(1).
APA	Dong,Qiao-Li,&Yuan,Han-bo.(2015).Accelerated Mann and CQ algorithms for finding a fixed point of a nonexpansive mapping.Fixed Point Theory and Applications,2015(1).
MLA	Dong,Qiao-Li,et al."Accelerated Mann and CQ algorithms for finding a fixed point of a nonexpansive mapping".Fixed Point Theory and Applications 2015.1(2015).