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

Classical algorithms are often not effective for solving nonconvex optimization problems
where local minima are separated by high barriers. In this paper, we explore possible …

Orthogonality constraints naturally appear in many machine learning problems, from
Principal Components Analysis to robust neural network training. They are usually solved …

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 …

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

Interior-point methods offer a highly versatile framework for convex optimization that is
effective in theory and practice. A key notion in their theory is that of a self-concordant …

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 …

Barycenters (aka Fréchet means) were introduced in statistics in the 1940's and popularized
in the fields of shape statistics and, later, in optimal transport and matrix analysis. They …

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

Deciding whether saddle points exist or are approximable for nonconvex-nonconcave
problems is usually intractable. This paper takes a step towards understanding a broad …