Andrew D. McRae

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math.OC2025

Sensor network localization has a benign landscape after low-dimensional relaxation

Christopher Criscitiello, Andrew D. McRae, Quentin Rebjock +1

We consider the sensor network localization problem, which is closely related to multidimensional scaling and Euclidean distance matrix completion. Given a ground truth configurati…

math.OC2025

Benign landscapes for synchronization on spheres via normalized Laplacian matrices

Andrew D. McRae

We study the nonconvex optimization landscapes of synchronization problems on spheres. First, we present new results for the statistical problem of synchronization over the two-ele…

math.OC2024

Nonconvex landscapes for $Z_{2}$ synchronization and graph clustering are benign near exact recovery thresholds

Andrew D. McRae, Pedro Abdalla, Afonso S. Bandeira +1

We study the optimization landscape of a smooth nonconvex program arising from synchronization over the two-element group $Z_{2}$ , that is, recovering $z_1, \dots, z_n \in \…

math.OC2024

Synchronization on circles and spheres with nonlinear interactions

Christopher Criscitiello, Quentin Rebjock, Andrew D. McRae +1

We consider the dynamics of $n$ points on a sphere in $R^{d}$ ( $d \geq 2$ ) which attract each other according to a function $φ$ of their inner products. When $φ$ is linear (…

Sensor network localization has a benign landscape after low-dimensional relaxation

Benign landscapes for synchronization on spheres via normalized Laplacian matrices

Nonconvex landscapes for Z2​ synchronization and graph clustering are benign near exact recovery thresholds

Synchronization on circles and spheres with nonlinear interactions

Nonconvex landscapes for $Z_{2}$ synchronization and graph clustering are benign near exact recovery thresholds