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 …

The conjugate gradient method is a crucial first-order optimization method that generally
converges faster than the steepest descent method, and its computational cost is much …

This paper is devoted to studying an augmented Lagrangian method for solving a class of
manifold optimization problems, which have nonsmooth objective functions and nonlinear …

Abstract Recently, the approximate Karush–Kuhn–Tucker (AKKT) conditions, also called the
sequential optimality conditions, have been proposed for nonlinear optimization in …

Contemporary advances in the field of deep learning have embarked upon an exploration of
the underlying geometric properties of data, thus encouraging the investigation of …

We propose an adaptive trust-region method for Riemannian optimization problems.
Especially, the trust-region radius converges to zero with the adaptive technique, and the …

The symplectic Stiefel manifold is a Riemannian manifold that is a generalization of the
symplectic group. In this letter, we propose novel conjugate gradient methods on the …

This study deals with Riemannian optimization on the unit sphere in terms of p-norm with
general p> 1. As a Riemannian submanifold of the Euclidean space, the geometry of the …

Riemannian optimization is concerned with problems, where the independent variable lies
on a smooth manifold. There is a number of problems from numerical linear algebra that fall …