Convergence of SDP hierarchies for polynomial optimization on the hypersphere
Optimization and Control
2013-06-25 v2 Data Structures and Algorithms
Mathematical Physics
math.MP
Quantum Physics
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.
Keywords
Cite
@article{arxiv.1210.5048,
title = {Convergence of SDP hierarchies for polynomial optimization on the hypersphere},
author = {Andrew C. Doherty and Stephanie Wehner},
journal= {arXiv preprint arXiv:1210.5048},
year = {2013}
}
Comments
45 pages, amsmath, comments welcome, for readers in quantum information: contains de Finetti theorem, v2: improved explanations, additional bound