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Geometric dual formulation for first-derivative-based univariate cubic L-1 splines
Zhao, Y. B.2; Fang, S. -C.1,3; Lavery, J. E.4
2008-04-01
Source PublicationJOURNAL OF GLOBAL OPTIMIZATION
ISSN0925-5001
Volume40Issue:4Pages:589-621
AbstractWith the objective of generating "shape-preserving" smooth interpolating curves that represent data with abrupt changes in magnitude and/or knot spacing, we study a class of first-derivative-based C-1-smooth univariate cubic L-1 splines. An L-1 spline minimizes the L-1 norm of the difference between the first-order derivative of the spline and the local divided difference of the data. Calculating the coefficients of an L-1 spline is a nonsmooth non-linear convex program. Via Fenchel's conjugate transformation, the geometric dual program is a smooth convex program with a linear objective function and convex cubic constraints. The dual-to-primal transformation is accomplished by solving a linear program.
Keywordconjugate function convex program cubic L-1 spline shape-preserving interpolation piecewise polynomial
DOI10.1007/s10898-006-9124-y
Language英语
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000253528100006
PublisherSPRINGER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/6669
Collection中国科学院数学与系统科学研究院
Corresponding AuthorFang, S. -C.
Affiliation1.N Carolina State Univ, Raleigh, NC 27695 USA
2.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100080, Peoples R China
3.Tsinghua Univ, Dept Math Sci & Ind Engn, Beijing 100084, Peoples R China
4.USA, Res Off, Res Lab, Div Math, Res Triangle Pk, NC 27709 USA
Recommended Citation
GB/T 7714
Zhao, Y. B.,Fang, S. -C.,Lavery, J. E.. Geometric dual formulation for first-derivative-based univariate cubic L-1 splines[J]. JOURNAL OF GLOBAL OPTIMIZATION,2008,40(4):589-621.
APA Zhao, Y. B.,Fang, S. -C.,&Lavery, J. E..(2008).Geometric dual formulation for first-derivative-based univariate cubic L-1 splines.JOURNAL OF GLOBAL OPTIMIZATION,40(4),589-621.
MLA Zhao, Y. B.,et al."Geometric dual formulation for first-derivative-based univariate cubic L-1 splines".JOURNAL OF GLOBAL OPTIMIZATION 40.4(2008):589-621.
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