On semidefinite bounds for maximization of a non-convex quadratic objective over the l1 unit ball

Mustafa Ç. Pinar; Marc Teboulle

RAIRO - Operations Research (2006)

  • Volume: 40, Issue: 3, page 253-265
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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Pinar, Mustafa Ç., and Teboulle, Marc. "On semidefinite bounds for maximization of a non-convex quadratic objective over the l1 unit ball." RAIRO - Operations Research 40.3 (2006): 253-265. <http://eudml.org/doc/249741>.

@article{Pinar2006,
abstract = { 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. },
author = {Pinar, Mustafa Ç., Teboulle, Marc},
journal = {RAIRO - Operations Research},
keywords = {Non-convex quadratic optimization; L1-norm constraint; semidefinite programming relaxation; duality.; non-convex quadratic optimization; -norm constraint; duality},
language = {eng},
month = {11},
number = {3},
pages = {253-265},
publisher = {EDP Sciences},
title = {On semidefinite bounds for maximization of a non-convex quadratic objective over the l1 unit ball},
url = {http://eudml.org/doc/249741},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Pinar, Mustafa Ç.
AU - Teboulle, Marc
TI - On semidefinite bounds for maximization of a non-convex quadratic objective over the l1 unit ball
JO - RAIRO - Operations Research
DA - 2006/11//
PB - EDP Sciences
VL - 40
IS - 3
SP - 253
EP - 265
AB - 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.
LA - eng
KW - Non-convex quadratic optimization; L1-norm constraint; semidefinite programming relaxation; duality.; non-convex quadratic optimization; -norm constraint; duality
UR - http://eudml.org/doc/249741
ER -

References

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