We propose computationally tractable accelerated first-order methods for Riemannian
optimization, extending the Nesterov accelerated gradient (NAG) method. For both …

From optimal transport to robust dimensionality reduction, many machine learning
applicationscan be cast into the min-max optimization problems over Riemannian manifolds …

We study the query complexity of geodesically convex (g-convex) optimization on a
manifold. To isolate the effect of that manifold's curvature, we primarily focus on hyperbolic …

In this paper, we consider optimization problems over closed embedded submanifolds of R
n, which are defined by the constraints c (x)= 0. We propose a class of constraint-dissolving …

Numerous applications in machine learning and data analytics can be formulated as
equilibrium computation over Riemannian manifolds. Despite the extensive investigation of …

Block coordinate descent is an optimization paradigm that iteratively updates one block of
variables at a time, making it quite amenable to big data applications due to its scalability …

We further research on the accelerated optimization phenomenon on Riemannian manifolds
by introducing accelerated global first-order methods for the optimization of $ L $-smooth …

We propose a globally-accelerated, first-order method for the optimization of smooth and
(strongly or not) geodesically-convex functions in a wide class of Hadamard manifolds. We …

We study the asymptotic properties of geodesically convex $ M $-estimation on non-linear
spaces. Namely, we prove that under very minimal assumptions besides geodesic convexity …

In this paper, we propose a convergence acceleration scheme for general Riemannian
optimization problems by extrapolating iterates on manifolds. We show that when the …