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

Variational inference (VI) seeks to approximate a target distribution $\pi $ by an element of a
tractable family of distributions. Of key interest in statistics and machine learning is Gaussian …

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

We consider the vector embedding problem. We are given a finite set of items, with the goal
of assigning a representative vector to each one, possibly under some constraints (such as …

Conjugate gradient methods are important first-order optimization algorithms both in
Euclidean spaces and on Riemannian manifolds. However, while various types of conjugate …

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 …

Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a
robust variant of the Wasserstein distance. Recent work suggests that this quantity is more …

The Wasserstein distance has become increasingly important in machine learning and deep
learning. Despite its popularity, the Wasserstein distance is hard to approximate because of …

We consider a class of nonsmooth optimization problems over the Stiefel manifold, in which
the objective function is weakly convex in the ambient Euclidean space. Such problems are …