Computing Minimal Interpolants in C^1,1(R^d)

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Article:

"Computing Minimal Interpolants in C^1,1(R^d)"

Ariel Herbert-Voss, Matthew J. Hirn, Frederick McCollum
Revista Mathematica Iberoamericana Vol. 33, Issue 1, (2017), pp. 29-66 

Link: http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=33&iss=1&rank=2

Abstract

We consider the following interpolation problem. Suppose one is given a finite set E ⊂ R^d, a function f: E → R, and possibly the gradients of f at the points of E. We want to interpolate the given information with a function F ∈ C^1,1(R^d) with the minimum possible value of Lip(∇F). We present practical, efficient algorithms for constructing an F such that Lip(∇F ) is minimal, or for less computational effort, within a small dimensionless constant of being minimal.