On Convex Quadratic Approximation

D. den Hertog; E. de Klerk; J. Roos

On Convex Quadratic Approximation

D. den Hertog, E. de Klerk, J. Roos

Research output: Working paper › Discussion paper › Other research output

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.

Original language	English
Place of Publication	Tilburg
Publisher	Operations research
Number of pages	12
Volume	2000-47
Publication status	Published - 2000

Publication series

Name	CentER Discussion Paper
Volume	2000-47

Keywords

Convex function
least squares
quadratic interpolation
semidefinite program- ming

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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.",

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AU - den Hertog, D.

AU - de Klerk, E.

AU - Roos, J.

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PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

KW - Convex function

KW - least squares

KW - quadratic interpolation

KW - semidefinite program- ming

M3 - Discussion paper

VL - 2000-47

T3 - CentER Discussion Paper

BT - On Convex Quadratic Approximation

PB - Operations research

CY - Tilburg

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