Accelerated Mann and CQ algorithms for finding a fixed point of a nonexpansive mapping
文献类型：期刊论文
| 作者 | Dong,Qiao-Li1,2; Yuan,Han-bo1 |
| 刊名 | Fixed Point Theory and Applications
 |
| 出版日期 | 2015-07-22 |
| 卷号 | 2015期号:1 |
| 关键词 | nonexpansive mapping convex minimization problem Picard algorithm Mann algorithm CQ algorithm conjugate gradient method steepest descent method |
| ISSN号 | 1687-1812 |
| DOI | 10.1186/s13663-015-0374-6 |
| 英文摘要 | 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. |
| 语种 | 英语 |
| WOS记录号 | BMC:10.1186/S13663-015-0374-6 |
| 出版者 | Springer International Publishing |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/338]  |
| 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). |
入库方式： OAI收割
来源：数学与系统科学研究院
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