Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 26, Issue 4, Pages 2355-2377Publisher
SIAM PUBLICATIONS
DOI: 10.1137/16M105808X
Keywords
angular synchronization; nonconvex optimization; generalized power method; projected power method; sufficient optimality conditions; quadratically constrained quadratic programming; optimization on manifolds
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Funding
- Fonds Speciaux de Recherche (FSR) from UCLouvain
- ERC Starting Grant SIPA
- Research in Paris grant
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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.
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