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

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

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Article ID: iaor20173359
Volume: 68
Issue: 1
Start Page Number: 95
End Page Number: 120
Publication Date: Sep 2017
Journal: Computational Optimization and Applications
Authors: , ,
Keywords: heuristics, programming: convex
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.

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