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

Mustafa Ç Pinar; Marc Teboulle

doi:10.1051/ro:2006023

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

Mustafa Ç Pinar^*, Marc Teboulle

^*Corresponding author for this work

School of Mathematical Sciences

Bilkent University

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	English
Pages (from-to)	253-265
Number of pages	13
Journal	RAIRO - Operations Research
Volume	40
Issue number	3
DOIs	https://doi.org/10.1051/ro:2006023
State	Published - 2006

Keywords

Duality
L1-norm constraint
Non-convex quadratic optimization
Semidefinite programming relaxation

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10.1051/ro:2006023

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KW - Semidefinite programming relaxation

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

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Keywords

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