Computational Optimization and Applications

, Volume 68, Issue 1, pp 95–120 | Cite as

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

  • Xavier Bay
  • Laurence Grammont
  • Hassan Maatouk


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.


Optimization RKHS Interpolation Inequality constraints 



The authors would like to thank the Associate Editor and the two anonymous referees for their helpful suggestions.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.École des Mines de Saint-ÉtienneSaint-Étienne Cedex 2France
  2. 2.UMR 5208, Institut Camille JordanUniversité de LyonSaint-Étienne Cedex 2France

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