5 papers
Smooth, globally Polyak-Åojasiewicz functions are nonlinear least-squares
Nicolas Boumal, Christopher Criscitiello, Quentin Rebjock
The Polyak-Åojasiewicz (PÅ) condition is often invoked in nonconvex optimization because it allows fast convergence of algorithms beyond strong convexity. A function $f \colon \m…
Negative curvature obstructs the existence of good barriers for interior-point methods
Christopher Criscitiello, Harold Nieuwboer, Michael Walter
Interior-point methods (IPMs) are a cornerstone of Euclidean convex optimization, due to their strong theoretical guarantees and practical performance. Motivated by scaling problem…
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…
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 (…
Horospherically Convex Optimization on Hadamard Manifolds Part I: Analysis and Algorithms
Christopher Criscitiello, Jungbin Kim
Geodesic convexity (g-convexity) is a natural generalization of convexity to Riemannian manifolds. However, g-convexity lacks many desirable properties satisfied by Euclidean conve…