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 …

In this paper we consider the minimization problem with constraints. We will show that if the
set of constraints is a Riemannian manifold of nonpositive sectional curvature, and the …

Experience gained during a ten-year long involvement in modelling, program ming and
application in nonlinear optimization helped me to arrive at the conclusion that in the interest …

Numerous problems in computer vision, pattern recognition, and machine learning are
formulated as optimization with manifold constraints. In this paper, we propose the Manifold …

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 …

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 …

This paper considers optimization problems on Riemannian manifolds and analyzes the
iteration-complexity for gradient and subgradient methods on manifolds with nonnegative …

We introduce a new nonsmooth variational model for the restoration of manifold-valued data
which includes second order differences in the regularization term. While such models were …

From optimal transport to robust dimensionality reduction, many machine learning
applicationscan be cast into the min-max optimization problems over Riemannian manifolds …