Low-rank modeling generally refers to a class of methods that solves problems by
representing variables of interest as low-rank matrices. It has achieved great success in …

Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus
is on problems where the smooth geometry of the search space can be leveraged to design …

As a paradigm to recover unknown entries of a matrix from partial observations, low-rank
matrix completion (LRMC) has generated a great deal of interest. Over the years, there have …

The matrix completion problem consists of finding or approximating a low-rank matrix based
on a few samples of this matrix. We propose a new algorithm for matrix completion that …

In tensor completion, the goal is to fill in missing entries of a partially known tensor under a
low-rank constraint. We propose a new algorithm that performs Riemannian optimization …

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 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 …

Matrix completion involves recovering a matrix from a subset of its entries by utilizing
interdependency between the entries, typically through low rank structure. Despite matrix …

We propose a novel geometric approach for learning bilingual mappings given monolingual
embeddings and a bilingual dictionary. Our approach decouples the source-to-target …

The aim of this paper is to derive convergence results for projected line-search methods on
the real-algebraic variety M_≤k of real m*n matrices of rank at most k. Such methods extend …