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ROBUST UNIVARIATE CUBIC L-2 SPINES: INTERPOLATING DATA WITH UNCERTAIN POSITIONS OF MEASUREMENTS
Averbakh, Igor1; Fang, Shu-Cherng2,3; Zhao, Yun-Bin4,5
2009-05-01
Source PublicationJOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
ISSN1547-5816
Volume5Issue:2Pages:351-361
AbstractTraditional univariate cubic spline models assume that the position and function value of each knot are given precisely. It has been observed that errors in data could result in significant fluctuations of the resulting spline. To handle situations that involve uncertainty only in measurements of function values, the concept of a robust spline has been developed in the literature. We propose a more general concept of a PH-robust cubic spline that takes into account also uncertainty in positions of measurements (knots or boundary points) using the paradigm of robust optimization. This bridges the robustness concepts developed in the interpolation/approximation and the optimization communities. Our model handles the case of "coordinated" variations of positions of measurements. It is formulated as a semi-infinite convex optimization problem. We develop a reformulation of the model as a finite explicit convex optimization problem, which makes it possible to use standard convex optimization algorithms for computation.
KeywordApproximation piecewise polynomial interpolation spline function robust optimization
DOI10.3934/jimo.2009.5.351
Language英语
WOS Research AreaEngineering ; Operations Research & Management Science ; Mathematics
WOS SubjectEngineering, Multidisciplinary ; Operations Research & Management Science ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000265190800012
PublisherAMER INST MATHEMATICAL SCIENCES
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/8927
Collection中国科学院数学与系统科学研究院
Corresponding AuthorAverbakh, Igor
Affiliation1.Univ Toronto, Div Management, Scarborough, ON M1C 1A4, Canada
2.N Carolina State Univ, Raleigh, NC 27695 USA
3.Tsinghua Univ, Dept Math Sci & Ind Engn, Beijing 100084, Peoples R China
4.Chinese Acad Sci, AMSS, Beijing, Peoples R China
5.Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England
Recommended Citation
GB/T 7714
Averbakh, Igor,Fang, Shu-Cherng,Zhao, Yun-Bin. ROBUST UNIVARIATE CUBIC L-2 SPINES: INTERPOLATING DATA WITH UNCERTAIN POSITIONS OF MEASUREMENTS[J]. JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION,2009,5(2):351-361.
APA Averbakh, Igor,Fang, Shu-Cherng,&Zhao, Yun-Bin.(2009).ROBUST UNIVARIATE CUBIC L-2 SPINES: INTERPOLATING DATA WITH UNCERTAIN POSITIONS OF MEASUREMENTS.JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION,5(2),351-361.
MLA Averbakh, Igor,et al."ROBUST UNIVARIATE CUBIC L-2 SPINES: INTERPOLATING DATA WITH UNCERTAIN POSITIONS OF MEASUREMENTS".JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 5.2(2009):351-361.
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