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l1-norm constraint

RAIRO - Operations Research (1)

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On semidefinite bounds for maximizationof a non-convex quadraticobjective over the l1 unit ball
Mustafa Ç. Pinar, Marc Teboulle
Journal:

RAIRO - Operations Research / Volume 40 / Issue 3 / July 2006

Published online by Cambridge University Press:

08 November 2006, pp. 253-265

Print publication:

July 2006
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We consider the non-convex quadratic maximization problem subjectto the l1 unit ball constraint. The nature of the l 1 normstructure makes this problem extremely hard to analyze, and as aconsequence, the same difficulties are encountered when trying tobuild suitable approximations for this problem by some tractableconvex counterpart formulations. We explore some properties ofthis problem, derive SDP-like relaxations and raise openquestions.