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.
- L1-norm constraint
- Non-convex quadratic optimization
- Semidefinite programming relaxation