Optimization on Riemannian manifolds-the result of smooth geometry and optimization
merging into one elegant modern framework-spans many areas of science and engineering …

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

Low-rank matrix estimation is a canonical problem that finds numerous applications in signal
processing, machine learning and imaging science. A popular approach in practice is to …

We establish theoretical recovery guarantees of a family of Riemannian optimization
algorithms for low rank matrix recovery, which is about recovering an m*n rank r matrix from …

We propose a novel Riemannian manifold preconditioning approach for the tensor
completion problem with rank constraint. A novel Riemannian metric or inner product is …

In recent years, stochastic variance reduction algorithms have attracted considerable
attention for minimizing the average of a large but finite number of loss functions. This paper …

We address the numerical problem of recovering large matrices of low rank when most of
the entries are unknown. We exploit the geometry of the low-rank constraint to recast the …

Low-rank matrix factorization (LRMF) is a canonical problem in non-convex optimization, the
objective function to be minimized is non-convex and even non-smooth, which makes the …

Discriminative subspace learning is an important problem in machine learning, which aims
to find the maximum separable decision subspace. Traditional Euclidean-based methods …

We propose a Riemannian version of Nesterov's Accelerated Gradient algorithm (\textsc
{Ragd}), and show that for\emph {geodesically} smooth and strongly convex problems …