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Convergence of SDP hierarchies for polynomial optimization on the hypersphere

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arxiv 1210.5048 v2 pith:E2QHXBJD submitted 2012-10-18 math.OC cs.DSmath-phmath.MPquant-ph

Andrew C. Doherty , Stephanie Wehner This is my paper · ORCID
classification math.OCcs.DSmath-phmath.MPquant-ph
keywords finettihypersphereoptimizationpolynomialquantumrelaxationsaccuracyapproximate
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. An Argmax Principle for Sum-of-Squares Relaxations on the Sphere

    cs.CC 2026-08 conditional novelty 7.0 of 10

    An argmax principle over high pseudo-moments yields degree-O(sqrt(n/eps)) SoS algorithms for Best Separable State, multiplicative 2->4 norm approximation, and a shorter proof of the known sphere-polynomial convergence bound.

  2. Some Applications and Limitations of Convex Optimization Hierarchies for Discrete and Continuous Optimization Problems

    cs.CC 2025-08 conditional novelty 7.0 of 10

    The thesis derives new approximation algorithms and conditional/unconditional lower bounds for CSPs, polynomial optimization over the sphere, and matrix p-to-q norms.

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