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

We consider optimization problems over the Stiefel manifold whose objective function is the
summation of a smooth function and a nonsmooth function. Existing methods for solving this …

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 …

We propose a new class of Riemannian conjugate gradient (CG) methods, in which inverse
retraction is used instead of vector transport for search direction construction. In existing …

In this paper we study nonconvex and nonsmooth multi-block optimization over Euclidean
embedded (smooth) Riemannian submanifolds with coupled linear constraints. Such …

In this paper we present a cubic regularized Newton's method to minimize a smooth function
over a Riemannian manifold. The proposed algorithm is shown to reach a second-order …

We develop a kernel projected Wasserstein distance for the two-sample test, an essential
building block in statistics and machine learning: given two sets of samples, to determine …

We consider optimization problems over the Stiefel manifold whose objective function is the
summation of a smooth function and a nonsmooth function. Existing methods for solving this …

This paper studies large-scale optimization problems on Riemannian manifolds whose
objective function is a finite sum of negative log-probability losses. Such problems arise in …