On Convex Quadratic Approximation

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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
Publication statusPublished - 2000

Publication series

NameCentER Discussion Paper


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


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