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

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 …

Detecting targets in dynamically changing clutter environments has always been
challenging for radar techniques. The innovative matrix information geometry-based (MIG) …

In this paper, we study Cayley-transform-based gradient and conjugate gradient algorithms
for optimization on Grassmann manifolds. We revisit the Cayley transform on Grassmann …

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 …

Nonlinear reformulations of the spectral clustering method have gained a lot of recent
attention due to their increased numerical benefits and their solid mathematical background …

We present a reformulation of optimization problems over the Stiefel manifold by using a
Cayley-type transform, named the generalized left-localized Cayley transform, for the Stiefel …

We study the convergence of the Riemannian steepest descent algorithm on the Grassmann
manifold for minimizing the block version of the Rayleigh quotient of a symmetric matrix …

Flag manifolds, sets of nested sequences of linear subspaces with fixed dimensions, are
rising in numerical analysis and statistics. The current optimization algorithms on flag …