The increasing integration of distributed energy resources calls for new planning and
operational tools. However, such tools depend on system topology and line parameters …

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 …

This article deals with the conjugate gradient method on a Riemannian manifold with
interest in global convergence analysis. The existing conjugate gradient algorithms on a …

In this paper, an optimization method for nonsmooth locally Lipschitz functions on complete
Riemannian manifolds is presented. The method is based on approximating the …

The problem of optimizing a quadratic form over an orthogonality constraint (QP-OC for
short) is one of the most fundamental matrix optimization problems and arises in many …

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, a Riemannian BFGS method for minimizing a smooth function on a
Riemannian manifold is defined, based on a Riemannian generalization of a cautious …

Adaptive regularization with cubics (ARC) is an algorithm for unconstrained, non-convex
optimization. Akin to the trust-region method, its iterations can be thought of as approximate …

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