Manifold optimization is ubiquitous in computational and applied mathematics, statistics,
engineering, machine learning, physics, chemistry, etc. One of the main challenges usually …

Mathematical optimization is an important branch of applied mathematics. Different classes
of optimization problems are categorized based on their problem structures. While there are …

In the Euclidean setting the proximal gradient method and its accelerated variants are a
class of efficient algorithms for optimization problems with decomposable objective. In this …

We propose the first global accelerated gradient method for Riemannian manifolds. Toward
establishing our results, we revisit Nesterov's estimate sequence technique and develop a …

Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian
inference literature, for their capacity to yield flexible and accurate approximations. We …

We propose a novel second-order ODE as the continuous-time limit of a Riemannian
accelerated gradient-based method on a manifold with curvature bounded from below. This …

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

The minimax optimization over Riemannian manifolds (possibly nonconvex constraints) has
been actively applied to solve many problems, such as robust dimensionality reduction and …

Abstract SPIDER (Stochastic Path Integrated Differential EstimatoR) is an efficient gradient
estimation technique developed for non-convex stochastic optimization. Although having …

We introduce Geomstats, an open-source Python package for computations and statistics on
nonlinear manifolds such as hyperbolic spaces, spaces of symmetric positive definite …