| Issue |
RAIRO-Oper. Res.
Volume 40, Number 3, July-September 2006
|
|
|---|---|---|
| Page(s) | 253 - 265 | |
| DOI | https://doi.org/10.1051/ro:2006023 | |
| Published online | 08 November 2006 | |
On semidefinite bounds for maximization of a non-convex quadratic objective over the l1 unit ball
1
Department of Industrial Engineering,Bilkent University, 06533 Ankara, Turkey; mustafap@bilkent.edu.tr
2
School of Mathematical Sciences,
Tel-Aviv University, Ramat-Aviv 69978, Israel; teboulle@math.tau.ac.il
Received:
25
June
2005
Accepted:
26
January
2006
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.
Key words: Non-convex quadratic optimization / L1-norm constraint / semidefinite programming relaxation / duality.
© EDP Sciences, 2006
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