IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v68y2017i1d10.1007_s10589-017-9906-9.html
   My bibliography  Save this article

A new method for interpolating in a convex subset of a Hilbert space

Author

Listed:
  • Xavier Bay

    (École des Mines de Saint-Étienne)

  • Laurence Grammont

    (Université de Lyon)

  • Hassan Maatouk

    (École des Mines de Saint-Étienne)

Abstract

In this paper, interpolating curve or surface with linear inequality constraints is considered as a general convex optimization problem in a Reproducing Kernel Hilbert Space. The aim of the present paper is to propose an approximation method in a very general framework based on a discretized optimization problem in a finite-dimensional Hilbert space under the same set of constraints. We prove that the approximate solution converges uniformly to the optimal constrained interpolating function. Numerical examples are provided to illustrate this result in the case of boundedness and monotonicity constraints in one and two dimensions.

Suggested Citation

  • Xavier Bay & Laurence Grammont & Hassan Maatouk, 2017. "A new method for interpolating in a convex subset of a Hilbert space," Computational Optimization and Applications, Springer, vol. 68(1), pages 95-120, September.
    • Handle: RePEc:spr:coopap:v:68:y:2017:i:1:d:10.1007_s10589-017-9906-9
    DOI: 10.1007/s10589-017-9906-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-017-9906-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-017-9906-9?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. H. Yin & Y. Wang & L. Qi, 2009. "Shape-Preserving Interpolation and Smoothing for Options Market Implied Volatility," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 243-266, July.
    Full references (including those not matched with items on IDEAS)

    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.
    1. Gianluca Cassese, 2015. "Nonparametric Estimates of Option Prices Using Superhedging," Working Papers 293, University of Milano-Bicocca, Department of Economics, revised Feb 2015.
    2. Gianluca Cassese, 2014. "Option Pricing in an Imperfect World," Papers 1406.0412, arXiv.org, revised Sep 2016.

    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:coopap:v:68:y:2017:i:1:d:10.1007_s10589-017-9906-9. 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.