Part 2 of this monograph builds on the introduction to tensor networks and their operations
presented in Part 1. It focuses on tensor network models for super-compressed higher-order …

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

We consider the minimization of a cost function f on a manifold using Riemannian gradient
descent and Riemannian trust regions (RTR). We focus on satisfying necessary optimality …

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

In this paper, a reconfigurable intelligent surface (RIS)-aided millimeter wave (mmWave)
non-orthogonal multiple access (NOMA) system is analyzed. In particular, we consider an …

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 …

We consider optimization problems on manifolds with equality and inequality constraints. A
large body of work treats constrained optimization in Euclidean spaces. In this work, we …

In the Euclidean setting the proximal gradient method and its accelerated variants are a
class of efficient algorithms for optimization problems with decomposable objective. In this …

We propose the first global accelerated gradient method for Riemannian manifolds. Toward
establishing our results, we revisit Nesterov's estimate sequence technique and develop a …

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 …