Croatian Operational Research Review (Dec 2010)
ON THE SET-SEMIDEFINITE REPRESENTATION OF NONCONVEX QUADRATIC PROGRAMS WITH CONE CONSTRAINTS
Abstract
The well-known result stating that any non-convex quadratic problem over the non-negative orthant with some additional linear and binary constraints can be rewritten as linear problem over the cone of completely positive matrices (Burer, 2009) is generalizes by replacing the non-negative orthant with arbitrary closed convex and pointed cone. This set-semidefinite representation result implies new semidefinite lower bounds for quadratic problems over the Bishop-Phelps cones, based on the Euclidian norm.
