Abstract
| 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 |
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Keywords
- Convex function
- least squares
- quadratic interpolation
- semidefinite program- ming
Cite this
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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 paper › Discussion paper › Other 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 -