IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v133y2005i1p229-24810.1007-s10479-004-5035-9.html
   My bibliography  Save this article

A Geometric Programming Framework for Univariate Cubic L 1 Smoothing Splines

Author

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

Abstract

Univariate cubic L 1 smoothing splines are capable of providing shape-preserving C 1 -smooth approximation of multi-scale data. The minimization principle for univariate cubic L 1 smoothing splines results in a nondifferentiable convex optimization problem that, for theoretical treatment and algorithm design, can be formulated as a generalized geometric program. In this framework, a geometric dual with a linear objective function over a convex feasible domain is derived, and a linear system for dual to primal conversion is established. Numerical examples are given to illustrate this approach. Sensitivity analysis for data with uncertainty is presented. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Hao Cheng & Shu-Cherng Fang & John Lavery, 2005. "A Geometric Programming Framework for Univariate Cubic L 1 Smoothing Splines," Annals of Operations Research, Springer, vol. 133(1), pages 229-248, January.
    • Handle: RePEc:spr:annopr:v:133:y:2005:i:1:p:229-248:10.1007/s10479-004-5035-9
    DOI: 10.1007/s10479-004-5035-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-004-5035-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-004-5035-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Elmor L. Peterson, 1977. "The Duality Between Suboptimization and Parameter Deletion," Discussion Papers 273, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Elmor L. Peterson, 1977. "The Duality between Suboptimization and Parameter Deletion," Mathematics of Operations Research, INFORMS, vol. 2(4), pages 311-319, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.
    2. Lu, Hao-Chun, 2020. "Indicator of power convex and exponential transformations for solving nonlinear problems containing posynomial terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    3. Han-Lin Li & Hao-Chun Lu, 2009. "Global Optimization for Generalized Geometric Programs with Mixed Free-Sign Variables," Operations Research, INFORMS, vol. 57(3), pages 701-713, June.
    4. Qingwei Jin & Lu Yu & John Lavery & Shu-Cherng Fang, 2012. "Univariate cubic L 1 interpolating splines based on the first derivative and on 5-point windows: analysis, algorithm and shape-preserving properties," Computational Optimization and Applications, Springer, vol. 51(2), pages 575-600, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:133:y:2005:i:1:p:229-248:10.1007/s10479-004-5035-9. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.