On Convex Quadratic Approximation

Research output: Working paperDiscussion paperOther research output

310 Downloads (Pure)

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 languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages12
Volume2000-47
Publication statusPublished - 2000

Publication series

NameCentER Discussion Paper
Volume2000-47

Fingerprint

Quadratic Approximation
Convex function
Least Squares Approximation
Multivariate Functions
Semidefinite Programming
Set of points
Univariate
Convexity
Finite Set
Statistics
Optimization

Keywords

  • Convex function
  • least squares
  • quadratic interpolation
  • semidefinite program- ming

Cite this

den Hertog, D., de Klerk, E., & Roos, J. (2000). On Convex Quadratic Approximation. (CentER Discussion Paper; Vol. 2000-47). Tilburg: Operations research.
den Hertog, D. ; de Klerk, E. ; Roos, J. / On Convex Quadratic Approximation. Tilburg : Operations research, 2000. (CentER Discussion Paper).
@techreport{18c7c3c6b40d41a593744c70223722b1,
title = "On Convex Quadratic Approximation",
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.",
keywords = "Convex function, least squares, quadratic interpolation, semidefinite program- ming",
author = "{den Hertog}, D. and {de Klerk}, E. and J. Roos",
note = "Pagination: 12",
year = "2000",
language = "English",
volume = "2000-47",
series = "CentER Discussion Paper",
publisher = "Operations research",
type = "WorkingPaper",
institution = "Operations research",

}

den Hertog, D, de Klerk, E & Roos, J 2000 'On Convex Quadratic Approximation' CentER Discussion Paper, vol. 2000-47, Operations research, Tilburg.

On Convex Quadratic Approximation. / den Hertog, D.; de Klerk, E.; Roos, J.

Tilburg : Operations research, 2000. (CentER Discussion Paper; Vol. 2000-47).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - On Convex Quadratic Approximation

AU - den Hertog, D.

AU - de Klerk, E.

AU - Roos, J.

N1 - Pagination: 12

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

ER -

den Hertog D, de Klerk E, Roos J. On Convex Quadratic Approximation. Tilburg: Operations research. 2000. (CentER Discussion Paper).