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Erratum to: ``On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets'' [Optim. Letters, 2012]

Peter J.C. Dickinson (P.J.C.Dickinson***at***rug.nl)
Gabriele Eichfelder (Gabriele.Eichfelder***at***tu-ilmenau.de)
Janez Povh (janez.povh***at***fis.unm.si)

Abstract: In this paper, an erratum is provided to the article ``\emph{On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets}'', published in Optim.\ Letters, 2012. Due to precise observation of the first author, it has been found that the proof of Lemma 9 has a nontrivial gap, and consequently the main result (Theorem 10) is incorrect. In this erratum, we prove that Corollary 14 is still correct in the original setting while to fix the proof of Theorem 10 we need additional assumptions. We provide a list of different commonly used assumptions making this theorem to be true, and a new version of this theorem, which is now Theorem 17.

Keywords: set-positivity, semide nite programming, copositive programming, quadratic con- straint, asymptotic cone

Category 1: Convex and Nonsmooth Optimization

Category 2: Linear, Cone and Semidefinite Programming

Citation: Faculty of information studies in Novo mesto, Ulica talcev 3, SI-8000, Novo mesto, 2012.

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Entry Submitted: 08/22/2012
Entry Accepted: 09/05/2012
Entry Last Modified: 07/04/2013

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