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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
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    References listed on IDEAS

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    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.
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