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On reformulations of nonconvex quadratic programs over convex cones by set-semidefinite constraints

Gabriele Eichfelder ( ♫ gabriele.eichfelder***at***am.uni-erlangen.de)
Janez Povh (Janez.povh***at***fis.unm.si)

Abstract: The well-known result stating that any non-convex quadratic problem over the nonnegative orthant with some additional linear and binary constraints can be rewritten as linear problem over the cone of completely positive matrices (Burer, 2009) is generalized by replacing the nonnegative orthant with an arbitrary closed convex cone. This set-semidefinite representation result implies new semidefinite lower bounds for quadratic problems over several Bishop-Phelps cones.

Keywords: set-positivity; Bishop-Phelps cone; semidefinite programming; copositive programming; mixed integer programming

Category 1: Convex and Nonsmooth Optimization

Category 2: Linear, Cone and Semidefinite Programming

Citation: Preprint No. 342, Institut fuer Angewandte Mathematik, Martensstraße 3, D-91058 Erlangen, ISSN 1435-5833, 2010

Download: [Postscript][PDF]

Entry Submitted: 12/09/2010
Entry Accepted: 12/09/2010
Entry Last Modified: 12/10/2010

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