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On semidefinite bounds for maximizationof 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 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.

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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