Andrew C. Doherty, Stephanie Wehner
Published 2012-10-18, updated 2013-06-22Version 2
We show how to bound the accuracy of a family of semi-definite programming relaxations for the problem of polynomial optimization on the hypersphere. Our method is inspired by a set of results from quantum information known as quantum de Finetti theorems. In particular, we prove a de Finetti theorem for a special class of real symmetric matrices to establish the existence of approximate representing measures for moment matrix relaxations.
Comments: 45 pages, amsmath, comments welcome, for readers in quantum information: contains de Finetti theorem, v2: improved explanations, additional bound
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