786 citations · 2.1k across the 35 of their papers we have counts for
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Non-Convex Phase Retrieval from STFT Measurements
Tamir Bendory, Yonina C. Eldar, Nicolas Boumal
The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases. We consider the closely-related…
The non-convex Burer-Monteiro approach works on smooth semidefinite programs
Nicolas Boumal, Vladislav Voroninski, Afonso S. Bandeira
Semidefinite programs (SDPs) can be solved in polynomial time by interior point methods, but scalability can be an issue. To address this shortcoming, over a decade ago, Burer and…
Global rates of convergence for nonconvex optimization on manifolds
Nicolas Boumal, P. -A. Absil, Coralia Cartis
We consider the minimization of a cost function on a manifold using Riemannian gradient descent and Riemannian trust regions (RTR). We focus on satisfying necessary optimal…
On the low-rank approach for semidefinite programs arising in synchronization and community detection
Afonso S. Bandeira, Nicolas Boumal, Vladislav Voroninski
To address difficult optimization problems, convex relaxations based on semidefinite programming are now common place in many fields. Although solvable in polynomial time, large se…
Nonconvex phase synchronization
Nicolas Boumal
We estimate phases (angles) from noisy pairwise relative phase measurements. The task is modeled as a nonconvex least-squares optimization problem. It was recently shown that t…