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

Xavier Bay (), Laurence Grammont () and Hassan Maatouk ()
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Xavier Bay: École des Mines de Saint-Étienne
Laurence Grammont: Université de Lyon
Hassan Maatouk: École des Mines de Saint-Étienne

Computational Optimization and Applications, 2017, vol. 68, issue 1, No 4, 95-120

Abstract: 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.

Keywords: Optimization; RKHS; Interpolation; Inequality constraints (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10589-017-9906-9

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