no. 3
On semidefinite bounds for maximization of a non-convex quadratic objective over the ℓ 1 unit ball
RAIRO - Operations Research - Recherche Opérationnelle, Tome 40 (2006) no. 3, pp. 253-265

We consider the non-convex quadratic maximization problem subject to the ℓ 1 unit ball constraint. The nature of the l 1 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.

DOI : 10.1051/ro:2006023
Keywords: non-convex quadratic optimization, L1-norm constraint, semidefinite programming relaxation, duality 
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     author = {Pinar, Mustafa \c{C}. and Teboulle, Marc},
     title = {On semidefinite bounds for maximization of a non-convex quadratic objective over the $\ell _1$ unit ball},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {253--265},
     year = {2006},
     publisher = {EDP Sciences},
     volume = {40},
     number = {3},
     doi = {10.1051/ro:2006023},
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Pinar, Mustafa Ç.; Teboulle, Marc. On semidefinite bounds for maximization of a non-convex quadratic objective over the $\ell _1$ unit ball. RAIRO - Operations Research - Recherche Opérationnelle, Tome 40 (2006) no. 3, pp. 253-265. doi: 10.1051/ro:2006023

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