On Convex Quadratic Approximation

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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Year of publication:	2000
Authors:	Den Hertog, Dick ; de Klerk, Etienne ; Roos, J.
Institutions:	Tilburg University, Center for Economic Research
Subject:	Convex function \| least squares \| quadratic interpolation \| semidefinite program- ming

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Extent:	application/pdf
Series:	Discussion Paper.
Type of publication:	Book / Working Paper
Notes:	The text is part of a series CentER Discussion Paper Number 2000-47
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011090460