ROBUST UNIVARIATE CUBIC L-2 SPINES: INTERPOLATING DATA WITH UNCERTAIN POSITIONS OF MEASUREMENTS

doi:10.3934/jimo.2009.5.351

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	ROBUST UNIVARIATE CUBIC L-2 SPINES: INTERPOLATING DATA WITH UNCERTAIN POSITIONS OF MEASUREMENTS
	Averbakh, Igor 1; Fang, Shu-Cherng 2,3; Zhao, Yun-Bin 4,5
	2009-05-01
发表期刊	JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
ISSN	1547-5816
卷号	5 期号:2 页码:351-361
摘要	Traditional 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.
关键词	Approximation piecewise polynomial interpolation spline function robust optimization
DOI	10.3934/jimo.2009.5.351
语种	英语
WOS研究方向	Engineering ; Operations Research & Management Science ; Mathematics
WOS类目	Engineering, Multidisciplinary ; Operations Research & Management Science ; Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000265190800012
出版者	AMER INST MATHEMATICAL SCIENCES
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8927
专题	中国科学院数学与系统科学研究院
通讯作者	Averbakh, Igor
作者单位	1.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
推荐引用方式 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.