Computing minimal interpolants in C^1,1(R^d)

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
We consider the following interpolation problem. Suppose one is given a finite set E R^d,a function f: ER, and possible the gradients of f at the points 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) is minimal, or for less computational effort, within a small dimensionless constant of being minimal.
http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=33&iss=1&rank=2