On Convex Quadratic Approximation

CentER Discussion Paper No. 2000-47

12 Pages Posted: 23 Oct 2000

See all articles by Dick den Hertog

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

Etienne de Klerk

Tilburg University

Kees Roos

Delft University of Technology - Faculty of Information Technology and Systems

Date Written: April 2000

Abstract

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

den Hertog, Dick and de Klerk, Etienne and Roos, Kees, On Convex Quadratic Approximation (April 2000). CentER Discussion Paper No. 2000-47. Available at SSRN: https://ssrn.com/abstract=247006 or http://dx.doi.org/10.2139/ssrn.247006

Dick Den Hertog

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Etienne De Klerk

Tilburg University ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Kees Roos

Delft University of Technology - Faculty of Information Technology and Systems

P.O. Box 5031
Department TWI/SSOR
2600 GA Delft
Netherlands

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