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NONCONVEX PHASE SYNCHRONIZATION

Author(s): Boumal, Nicolas

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dc.contributor.authorBoumal, Nicolas-
dc.date.accessioned2019-08-29T17:01:39Z-
dc.date.available2019-08-29T17:01:39Z-
dc.date.issued2016en_US
dc.identifier.citationBoumal, Nicolas. (2016). NONCONVEX PHASE SYNCHRONIZATION. SIAM JOURNAL ON OPTIMIZATION, 26 (2355 - 2377. doi:10.1137/16M105808Xen_US
dc.identifier.issn1052-6234-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1tb2m-
dc.description.abstractWe estimate n phases (angles) from noisy pairwise relative phase measurements. The task is modeled as a nonconvex least-squares optimization problem. It was recently shown that this problem can be solved in polynomial time via convex relaxation, under some conditions on the noise. In this paper, under similar but more restrictive conditions, we show that a modified version of the power method converges to the global optimum. This is simpler and (empirically) faster than convex approaches. Empirically, they both succeed in the same regime. Further analysis shows that, in the same noise regime as previously studied, second-order necessary optimality conditions for this quadratically constrained quadratic program are also sufficient, despite nonconvexity.en_US
dc.format.extent2355 - 2377en_US
dc.language.isoen_USen_US
dc.relation.ispartofSIAM JOURNAL ON OPTIMIZATIONen_US
dc.rightsFinal published version. Article is made available in OAR by the publisher's permission or policy.en_US
dc.titleNONCONVEX PHASE SYNCHRONIZATIONen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1137/16M105808X-
dc.date.eissued2016-11-01en_US
dc.identifier.eissn1095-7189-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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