Substantial progress has been made recently on develo** provably accurate and efficient
algorithms for low-rank matrix factorization via nonconvex optimization. While conventional …

We consider the problem of recovering a complete (ie, square and invertible) matrix A 0,
from Y∈ R n× p with Y= A 0 X 0, provided X 0 is sufficiently sparse. This recovery problem is …

Optimization on Riemannian manifolds-the result of smooth geometry and optimization
merging into one elegant modern framework-spans many areas of science and engineering …

We provide the first global optimization landscape analysis of Neural Collapse--an intriguing
empirical phenomenon that arises in the last-layer classifiers and features of neural …

Owing to their connection with generative adversarial networks (GANs), saddle-point
problems have recently attracted considerable interest in machine learning and beyond. By …

Gradient Descent Only Converges to Minimizers Page 1 JMLR: Workshop and Conference
Proceedings vol 49:1–12, 2016 Gradient Descent Only Converges to Minimizers Jason D. Lee …

We establish that first-order methods avoid strict saddle points for almost all initializations.
Our results apply to a wide variety of first-order methods, including (manifold) gradient …

We consider the minimization of a cost function f on a manifold using Riemannian gradient
descent and Riemannian trust regions (RTR). We focus on satisfying necessary optimality …

Geodesic convexity generalizes the notion of (vector space) convexity to nonlinear metric
spaces. But unlike convex optimization, geodesically convex (g-convex) optimization is …

We study optimization of finite sums of\emph {geodesically} smooth functions on
Riemannian manifolds. Although variance reduction techniques for optimizing finite-sums …