Convergence of SDP hierarchies for polynomial optimization on the hypersphere

Andrew C. Doherty; Stephanie Wehner

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arXiv · 1210.5048

Convergence of SDP hierarchies for polynomial optimization on the hypersphere

Andrew C. Doherty·Stephanie Wehner

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Abstract

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.

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Andrew C. Doherty, Stephanie Wehner. 2013-06-22. Convergence of SDP hierarchies for polynomial optimization on the hypersphere. https://arxiv.org/abs/1210.5048

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