A note on set-semidefinite relaxations of nonconvex quadratic programs

Authors:
Faizan Ahmed;Georg Still
Affiliations:
Department of Applied Mathematics, University of Twente, Enschede, The Netherlands 7500 AE;Department of Applied Mathematics, University of Twente, Enschede, The Netherlands 7500 AE
Venue:
Journal of Global Optimization
Year:
2013

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Abstract

We consider semidefinite, copositive, and more general, set-semidefinite programming relaxations of general nonconvex quadratic problems. For the semidefinite case a comparison between the feasible set of the original program and the feasible set of the relaxation has been given by Kojima and Tunçel (SIAM J Optim 10(3):750---778, 2000). In this paper the comparison is presented for set-positive relaxations which contain copositive relaxations as a special case.