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

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

We propose a new globalization strategy of the damped Newton method for finding
singularities of a vector field on Riemannian manifolds. We establish its global convergence …

When optimizing on a Riemannian manifold, it is important to use an efficient retraction,
which maps a point on a tangent space to a point on the manifold. In this paper, we prove a …

Sufficient dimension reduction (SDR) using distance covariance (DCOV) was recently
proposed as an approach to dimension-reduction problems. Compared with other SDR …

In this paper, we consider the problem of computing an arbitrary generalized singular value
of a Grassman or real matrix pair and a triplet of associated generalized singular vectors …

The l parameterized generalized eigenvalue problems for the nonsquare matrix pencils,
proposed by Chu et al. in 2006, can be formulated as an optimization problem on a …

The main tool to study a second order optimality problem is the Hessian operator associated
to the cost function that defines the optimization problem. By regarding an orthogonal Stiefel …

High-dimensional nonlinear optimization problems subject to nonlinear constraints can
appear in several contexts including constrained physical and dynamical systems, statistical …

This paper develops two novel and fast Riemannian second‐order approaches for solving a
class of matrix trace minimization problems with orthogonality constraints, which is widely …