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Univariate cubic L 1 splines – A geometric programming approach

Author

Listed:
  • Hao Cheng
  • Shu-Cherng Fang
  • John E. Lavery

Abstract

Univariate cubic L 1 splines provide C 1 -smooth, shape-preserving interpolation of arbitrary data, including data with abrupt changes in spacing and magnitude. The minimization principle for univariate cubic L 1 splines results in a nondifferentiable convex optimization problem. In order to provide theoretical treatment and to develop efficient algorithms, this problem is reformulated as a generalized geometric programming problem. A geometric dual with a linear objective function and convex quadratic constraints is derived. A linear system for dual to primal conversion is established. The results of computational experiments are presented. In the natural norm for this class of problems, namely, the L 1 norm of the second derivative, the geometric programming approach finds better solutions than the previously used discretization method. Copyright Springer-Verlag Berlin Heidelberg 2002

Suggested Citation

  • Hao Cheng & Shu-Cherng Fang & John E. Lavery, 2002. "Univariate cubic L 1 splines – A geometric programming approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(2), pages 197-229, November.
    • Handle: RePEc:spr:mathme:v:56:y:2002:i:2:p:197-229
    DOI: 10.1007/s001860200216
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    Cited by:

    1. Chiu, Nan-Chieh & Fang, Shu-Cherng & Lavery, John E. & Lin, Jen-Yen & Wang, Yong, 2008. "Approximating term structure of interest rates using cubic L1 splines," European Journal of Operational Research, Elsevier, vol. 184(3), pages 990-1004, February.

    More about this item

    Keywords

    Key words: cubic L1 spline; geometric programming; interpolation; spline function; univariate;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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