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

Mustafa Ç Pinar, Marc Teboulle

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)253-265
Number of pages13
JournalRAIRO - Operations Research
Volume40
Issue number3
DOIs
StatePublished - Jul 2006

Keywords

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

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