We study sampling as optimization in the space of measures. We focus on gradient flow-
based optimization with the Langevin dynamics as a case study. We investigate the source …

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 maximal monotonicity notion in Banach spaces is extended to Riemannian manifolds of
nonpositive sectional curvature, Hadamard manifolds, and proved to be equivalent to the …

The proximal point algorithm, which is a well-known tool for finding minima of convex
functions, is generalized from the classical Hilbert space framework into a nonlinear setting …

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 …

The notion of variational inequalities is extended to Hadamard manifolds and related to
geodesic convex optimization problems. Existence and uniqueness theorems for variational …

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 …

An equilibrium theory is developed in Hadamard manifolds. The existence of equilibrium
points for a bifunction is proved under suitable conditions, and applications to variational …

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 …

Many modern machine learning applications-from online principal component analysis to
covariance matrix identification and dictionary learning-can be formulated as minimization …