Multivariate Convex Approximation and Least-Norm Convex Data-Smoothing

CentER Discussion Paper Series No. 2005-132

14 Pages Posted: 17 Jan 2006

See all articles by A.Y.D. Siem

A.Y.D. Siem

Tilburg University - Department of Econometrics & Operations Research

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

A. L. Hoffmann

Radboud University Nijmegen - Faculty of Medical Sciences

Date Written: December 2005

Abstract

The main contents of this paper is two-fold. First, we present a method to approximate multivariate convex functions by piecewise linear upper and lower bounds. We consider a method that is based on function evaluations only. However, to use this method, the data have to be convex. Unfortunately, even if the underlying function is convex, this is not always the case due to (numerical) errors.Therefore, secondly, we present a multivariate data-smoothing method that smooths nonconvex data. We consider both the case that we have only function evaluations and the case that we also have derivative information.Furthermore, we show that our methods are polynomial time methods. We illustrate this methodology by applying it to some examples.

Keywords: approximation theory; convexity; data-smoothing

JEL Classification: C60

Suggested Citation

Siem, A.Y.D. and den Hertog, Dick and Hoffmann, A. L., Multivariate Convex Approximation and Least-Norm Convex Data-Smoothing (December 2005). Available at SSRN: https://ssrn.com/abstract=875615 or http://dx.doi.org/10.2139/ssrn.875615

A.Y.D. Siem (Contact Author)

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

P.O.Box 90153
5000 LE Tilburg
Netherlands

Dick Den Hertog

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

Tilburg, 5000 LE
Netherlands

A. L. Hoffmann

Radboud University Nijmegen - Faculty of Medical Sciences ( email )

Nijmegen, NL-6500 HB
Netherlands

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