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

We study projection-free methods for constrained Riemannian optimization. In particular, we
propose a Riemannian Frank-Wolfe (rfw) method that handles constraints directly, in …

Optimization on Riemannian manifolds widely arises in eigenvalue computation, density
functional theory, Bose--Einstein condensates, low rank nearest correlation, image …

The low-rank matrix completion problem can be solved by Riemannian optimization on a
fixed-rank manifold. However, a drawback of the known approaches is that the rank …

The symplectic Stiefel manifold, denoted by Sp(2p,2n), is the set of linear symplectic maps
between the standard symplectic spaces R^2p and R^2n. When p=n, it reduces to the well …

We propose Riemannian preconditioned algorithms for the tensor completion problem via
tensor ring decomposition. A new Riemannian metric is developed on the product space of …

Signed networks allow to model positive and negative relationships. We analyze existing
extensions of spectral clustering to signed networks. It turns out that existing approaches do …

Projection robust Wasserstein (PRW) distance is recently proposed to efficiently mitigate the
curse of dimensionality in the classical Wasserstein distance. In this paper, by equivalently …

Algorithms for the computation of the (weighted) geometric mean G of two positive definite
matrices are described and discussed. For large and sparse matrices the problem of …

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