KMS Of Academy of mathematics and systems sciences, CAS
| Accelerated Mann and CQ algorithms for finding a fixed point of a nonexpansive mapping | |
| Dong,Qiao-Li1,2; Yuan,Han-bo1 | |
| 2015-07-22 | |
| Source Publication | Fixed Point Theory and Applications
 |
| ISSN | 1687-1812 |
| Volume | 2015Issue:1 |
| Abstract | 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. |
| Keyword | nonexpansive mapping convex minimization problem Picard algorithm Mann algorithm CQ algorithm conjugate gradient method steepest descent method |
| DOI | 10.1186/s13663-015-0374-6 |
| Language | 英语 |
| WOS ID | BMC:10.1186/s13663-015-0374-6 |
| Publisher | Springer International Publishing |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/339 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Dong,Qiao-Li |
| Affiliation | 1.Civil Aviation University of China; College of Science 2.Civil Aviation University of China; Tianjin Key Lab for Advanced Signal Processing |
| Recommended Citation 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). |
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