A new semidefinite programming relaxation scheme for a class of quadratic matrix problems

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Abstract

We consider a special class of quadratic matrix optimization problems which often arise in applications. By exploiting the special structure of these problems, we derive a new semidefinite relaxation which, under mild assumptions, is proven to be tight for a larger number of constraints than could be achieved via a direct approach. We show the potential usefulness of these results when applied to robust least-squares and sphere-packing problems.

Original languageEnglish
Pages (from-to)298-302
Number of pages5
JournalOperations Research Letters
Volume40
Issue number4
DOIs
StatePublished - Jul 2012

Keywords

  • Homogenization
  • Nonconvex quadratic optimization
  • Rank reduction
  • Semidefinite relaxations
  • Strong duality

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