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

Published online by Cambridge University Press:  08 November 2006

Mustafa Ç. Pinar  and
Marc Teboulle
Mustafa Ç. Pinar
Affiliation:
Department of Industrial Engineering,Bilkent University, 06533 Ankara, Turkey; mustafap@bilkent.edu.tr
Marc Teboulle
Affiliation:
School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel; teboulle@math.tau.ac.il
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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.

Keywords

Non-convex quadratic optimizationL1-norm constraintsemidefinite programming relaxationduality.
Type
Research Article
Information
RAIRO - Operations Research , Volume 40 , Issue 3 , July 2006 , pp. 253 - 265
Copyright
© EDP Sciences, 2006

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