The Grassmann manifold of linear subspaces is important for the mathematical modelling of
a multitude of applications, ranging from problems in machine learning, computer vision and …

In this work, we consider monotone Riemannian Variational Inequality Problems (RVIPs),
which encompass both Riemannian convex optimization and minimax optimization as …

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 …

To explore convex optimization on Hadamard spaces, we consider an iteration in the style of
a subgradient algorithm. Traditionally, such methods assume that the underlying spaces are …

In this work, we analyze two of the most fundamental algorithms in geodesically convex
optimization: Riemannian gradient descent and (possibly inexact) Riemannian proximal …

Many of the primal ingredients of convex optimization extend naturally from Euclidean to
Hadamard spaces $\unicode {x2014} $ nonpositively curved metric spaces like Euclidean …

This thesis is concerned with scaling problems, which have been of much interest in recent
years. It is a class of computational problems with a plethora of connections to different …