ROBUST UNIVARIATE CUBIC L-2 SPINES: INTERPOLATING DATA WITH UNCERTAIN POSITIONS OF MEASUREMENTS
文献类型：期刊论文
| 作者 | Averbakh, Igor1; Fang, Shu-Cherng2,3; Zhao, Yun-Bin4,5 |
| 刊名 | JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
 |
| 出版日期 | 2009-05-01 |
| 卷号 | 5期号:2页码:351-361 |
| 关键词 | Approximation piecewise polynomial interpolation spline function robust optimization |
| ISSN号 | 1547-5816 |
| DOI | 10.3934/jimo.2009.5.351 |
| 英文摘要 | 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. |
| WOS研究方向 | Engineering ; Operations Research & Management Science ; Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000265190800012 |
| 出版者 | AMER INST MATHEMATICAL SCIENCES |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/8926]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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