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.
Preprint No. 342, Institut fuer Angewandte Mathematik, Martensstraße 3, D-91058 Erlangen, ISSN 1435-5833, 2010
View On reformulations of nonconvex quadratic programs over convex cones by set-semidefinite constraints