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

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

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Article ID: iaor20072605
Country: France
Volume: 40
Issue: 3
Start Page Number: 253
End Page Number: 265
Publication Date: Jul 2006
Journal: RAIRO Operations Research
Authors: ,
Keywords: duality, programming (semidefinite)
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.

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