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

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 …

Mathematical optimization is an important branch of applied mathematics. Different classes
of optimization problems are categorized based on their problem structures. While there are …

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 develop a manifold inexact augmented Lagrangian framework to solve a family of
nonsmooth optimization problem on Riemannian submanifold embedding in Euclidean …

This paper focuses on the minimization of a possibly nonsmooth objective function over the
Stiefel manifold. The existing approaches either lack efficiency or can only tackle prox …

Block coordinate descent is an optimization paradigm that iteratively updates one block of
variables at a time, making it quite amenable to big data applications due to its scalability …

We consider the problem of minimizing the sum of a smooth nonconvex function and a
nonsmooth convex function over a compact embedded submanifold. We describe an …