153 citations · 157 across the 5 of their papers we have counts for
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Smooth, globally Polyak-Łojasiewicz functions are nonlinear least-squares
Nicolas Boumal, Christopher Criscitiello, Quentin Rebjock
The Polyak-Łojasiewicz (PŁ) condition is often invoked in nonconvex optimization because it allows fast convergence of algorithms beyond strong convexity. A function $f \colon \mat…
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…
Optimization over bounded-rank matrices through a desingularization enables joint global and local guarantees
Quentin Rebjock, Nicolas Boumal
Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a nonsmooth and nonconvex algebraic variety. Existing techniqu…
Synchronization on circles and spheres with nonlinear interactions
Christopher Criscitiello, Quentin Rebjock, Andrew D. McRae +1
We consider the dynamics of points on a sphere in () which attract each other according to a function of their inner products. When is linear (…
Fast convergence of trust-regions for non-isolated minima via analysis of CG on indefinite matrices
Quentin Rebjock, Nicolas Boumal
Trust-region methods (TR) can converge quadratically to minima where the Hessian is positive definite. However, if the minima are not isolated, then the Hessian there cannot be pos…