On Convex Quadratic Approximation
CentER Discussion Paper No. 2000-47
12 Pages Posted: 23 Oct 2000
Date Written: April 2000
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of statistics and optimization. We show that convexity can be enforced in the multivariate case by using semidefinite programming techniques.
Key words: Convex function, least squares, quadratic interpolation, semidefinite programming
Suggested Citation: Suggested Citation