Ellipsoidal Arithmetic for Multivariate Systems
Villanueva, M. E.1; Rajyaguru, J.1; Houska, B.2; Chachuat, B.1
2015
Source Publication12TH INTERNATIONAL SYMPOSIUM ON PROCESS SYSTEMS ENGINEERING (PSE) AND 25TH EUROPEAN SYMPOSIUM ON COMPUTER AIDED PROCESS ENGINEERING (ESCAPE), PT A
Volume37
Pages767-772
Status已发表
AbstractThe ability to determine enclosures for the image set of nonlinear functions is pivotal to many applications in engineering. This paper presents a method for the systematic construction of ellipsoidal extensions of factorable functions. It proceeds by lifting the ellipsoid to a higher dimensional space for every atom operation in the function's directed acyclic graph, thereby accounting for dependencies. We present theoretical results regarding the quadratic Hausdorff convergence of the computed enclosures. Moreover, we propose an efficient implementation, whereby the shape matrix of the lifted ellipsoid is stored in sparse format, and every atom operation corresponds to a sparse update in that matrix. We illustrate these developments with two numerical examples.
KeywordEllipsoids Function Bounding Interval Arithmetic
Publication PlaceSARA BURGERHARTSTRAAT 25, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
Indexed ByCPCI
Language英语
WOS Research AreaEngineering
WOS SubjectEngineering, Chemical ; Engineering, Industrial
WOS IDWOS:000366889500123
PublisherELSEVIER SCIENCE BV
WOS KeywordINTERVAL-ANALYSIS ; GLOBAL OPTIMIZATION
Original Document TypeProceedings Paper
Document Type会议论文
Identifierhttp://kms.shanghaitech.edu.cn/handle/2MSLDSTB/2306
Collection信息科学与技术学院_PI研究组_Boris Houska组
Corresponding AuthorVillanueva, M. E.
Affiliation1.Univ London Imperial Coll Sci Technol & Med, Ctr Proc Syst Engn, London SW7 2AZ, England
2.ShanghaiTech Univ, Sch Informat Sci & Technol, Shanghai 200031, Peoples R China
Recommended Citation
GB/T 7714
Villanueva, M. E.,Rajyaguru, J.,Houska, B.,et al. Ellipsoidal Arithmetic for Multivariate Systems[C]. SARA BURGERHARTSTRAAT 25, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS:ELSEVIER SCIENCE BV,2015:767-772.
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