ShanghaiTech University Knowledge Management System
Chebyshev model arithmetic for factorable functions | |
Rajyaguru, Jai1; Villanueva, Mario E.1; Houska, Boris2; Chachuat, Benoit1 | |
2017-06 | |
发表期刊 | JOURNAL OF GLOBAL OPTIMIZATION |
ISSN | 0925-5001 |
卷号 | 68期号:2页码:413-438 |
发表状态 | 已发表 |
DOI | 10.1007/s10898-016-0474-9 |
摘要 | This article presents an arithmetic for the computation of Chebyshev models for factorable functions and an analysis of their convergence properties. Similar to Taylor models, Chebyshev models consist of a pair of a multivariate polynomial approximating the factorable function and an interval remainder term bounding the actual gap with this polynomial approximant. Propagation rules and local convergence bounds are established for the addition, multiplication and composition operations with Chebyshev models. The global convergence of this arithmetic as the polynomial expansion order increases is also discussed. A generic implementation of Chebyshev model arithmetic is available in the library MC++. It is shown through several numerical case studies that Chebyshev models provide tighter bounds than their Taylor model counterparts, but this comes at the price of extra computational burden. |
关键词 | Global optimization Factorable functions Chebyshev models Taylor models Interval analysis Convergence rate |
收录类别 | SCI ; EI |
语种 | 英语 |
资助项目 | Engineering and Physical Sciences Research Council (EPSRC)[EP/J006572/1] |
WOS研究方向 | Operations Research & Management Science ; Mathematics |
WOS类目 | Operations Research & Management Science ; Mathematics, Applied |
WOS记录号 | WOS:000401476700009 |
出版者 | SPRINGER |
EI入藏号 | 20164202916907 |
EI主题词 | Global optimization |
WOS关键词 | DETERMINISTIC GLOBAL OPTIMIZATION ; POLYNOMIAL MULTIPLICATION ; CONVEX UNDERESTIMATORS ; CLUSTER PROBLEM ; RELAXATIONS ; EXTENSION |
原始文献类型 | Article |
通讯作者 | Chachuat, Benoit |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/1351 |
专题 | 信息科学与技术学院_PI研究组_Boris Houska组 |
通讯作者 | Chachuat, Benoit |
作者单位 | 1.Imperial Coll London, Dept Chem Engn, Ctr Proc Syst Engn, South Kensington Campus, London SW7 2AZ, England 2.ShanghaiTech Univ, Sch Informat Sci & Technol, 319 Yueyang Rd, Shanghai 200031, Peoples R China |
推荐引用方式 GB/T 7714 | Rajyaguru, Jai,Villanueva, Mario E.,Houska, Boris,et al. Chebyshev model arithmetic for factorable functions[J]. JOURNAL OF GLOBAL OPTIMIZATION,2017,68(2):413-438. |
APA | Rajyaguru, Jai,Villanueva, Mario E.,Houska, Boris,&Chachuat, Benoit.(2017).Chebyshev model arithmetic for factorable functions.JOURNAL OF GLOBAL OPTIMIZATION,68(2),413-438. |
MLA | Rajyaguru, Jai,et al."Chebyshev model arithmetic for factorable functions".JOURNAL OF GLOBAL OPTIMIZATION 68.2(2017):413-438. |
条目包含的文件 | 下载所有文件 | |||||
文件名称/大小 | 文献类型 | 版本类型 | 开放类型 | 使用许可 |
修改评论
除非特别说明,本系统中所有内容都受版权保护,并保留所有权利。