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

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. We propose a new approximation method 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. An algorithm is derived and numerical examples with boundedness and mono-tonicity constraints in one and two dimensions are given.
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Submitted on : Wednesday, December 30, 2015 - 10:11:58 AM
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Xavier Bay, Laurence Grammont, Hassan Maatouk. A new method for interpolating in a convex subset of a Hilbert space. Computational Optimization and Applications, Springer Verlag, 2017, 68 (1), pp.95-120. ⟨http://link.springer.com/article/10.1007/s10589-017-9906-9⟩. ⟨10.1007/s10589-017-9906-9⟩. ⟨hal-01136466v2⟩

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