34 citations · 38 across the 11 of their papers we have counts for
11 papers
Doubling the dimension yields a benign landscape for the squared-stress
Christopher Criscitiello
We consider the Euclidean distance geometry problem (EDG): given a subset of the pairwise distances of an unknown cloud of points in , recover the point cloud…
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…
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…
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…
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 (…
Open Problem: Polynomial linearly-convergent method for geodesically convex optimization?
Christopher Criscitiello, David Martínez-Rubio, Nicolas Boumal
Let be a Lipschitz and geodesically convex function defined on a -dimensional Riemannian manifold . Does there exist a first-o…
Accelerated Methods for Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties
David Martínez-Rubio, Christophe Roux, Christopher Criscitiello +1
In this work, we study optimization problems of the form , where is defined on a product Riemannian manifold and i…
Negative curvature obstructs acceleration for strongly geodesically convex optimization, even with exact first-order oracles
Christopher Criscitiello, Nicolas Boumal
Hamilton and Moitra (2021) showed that, in certain regimes, it is not possible to accelerate Riemannian gradient descent in the hyperbolic plane if we restrict ourselves to algorit…
An accelerated first-order method for non-convex optimization on manifolds
Christopher Criscitiello, Nicolas Boumal
We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessi…
Efficiently escaping saddle points on manifolds
Chris Criscitiello, Nicolas Boumal
Smooth, non-convex optimization problems on Riemannian manifolds occur in machine learning as a result of orthonormality, rank or positivity constraints. First- and second-order ne…