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
ISSN0925-5001
卷号68期号:2页码:413-438
发表状态已发表
DOI10.1007/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.
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