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 …

Conjugate gradient methods are important first-order optimization algorithms both in
Euclidean spaces and on Riemannian manifolds. However, while various types of conjugate …

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

In this paper we propose a new Riemannian conjugate gradient method for optimization on
the Stiefel manifold. We introduce two novel vector transports associated with the retraction …

In this paper, we study min-max optimization problems on Riemannian manifolds. We
introduce a Riemannian Hamiltonian function, minimization of which serves as a proxy for …

Riemannian optimization is the task of finding an optimum of a real-valued function defined
on a Riemannian manifold. Riemannian optimization has been a topic of much interest over …

In this paper, we focus on the decentralized optimization problem over the Stiefel manifold,
which is defined on a connected network of agents. The objective is an average of local …

Nonsmooth Riemannian optimization is still a scarcely explored subfield of optimization
theory that concerns the general problem of minimizing (or maximizing) over a domain …

We propose a new class of Riemannian conjugate gradient (CG) methods, in which inverse
retraction is used instead of vector transport for search direction construction. In existing …