Skip to main content


Author(s): Boumal, Nicolas

To refer to this page use:
Abstract: We 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.
Publication Date: 2016
Electronic Publication Date: 1-Nov-2016
Citation: Boumal, Nicolas. (2016). NONCONVEX PHASE SYNCHRONIZATION. SIAM JOURNAL ON OPTIMIZATION, 26 (2355 - 2377. doi:10.1137/16M105808X
DOI: doi:10.1137/16M105808X
ISSN: 1052-6234
EISSN: 1095-7189
Pages: 2355 - 2377
Type of Material: Journal Article
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.