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We consider the non-convex quadratic maximization problem subject to the ℓ1 unit ball constraint. The nature of the l1 norm structure makes this problem extremely hard to analyze, and as a consequence, the same difficulties are encountered when trying to build suitable approximations for this problem by some tractable convex counterpart formulations. We explore some properties of this problem, derive SDP-like relaxations and raise open questions. © EDP Sciences 2006

On semidefinite bounds for maximization of a non-convex quadratic objective over thel1unit ball

On semidefinite bounds for maximization of a non-convex quadratic objective over thel₁unit ball