11 citations · 13 across the 5 of their papers we have counts for
10 papers
A Riemannian gradient descent method for optimization on the indefinite Stiefel manifold
Dinh Van Tiep, Nguyen Thanh Son
We consider the optimization problem with a generally quadratic matrix constraint of the form , where is a given nonsingular, symmetric matrix and is…
Symplectic Stiefel manifold: tractable metrics, second-order geometry and Newton's methods
Bin Gao, Nguyen Thanh Son, Tatjana Stykel
Optimization under the symplecticity constraint is an approach for solving various problems in quantum physics and scientific computing. Building on the results that this optimizat…
Optimization on the symplectic Stiefel manifold: SR decomposition-based retraction and applications
Bin Gao, Nguyen Thanh Son, Tatjana Stykel
Numerous problems in optics, quantum physics, stability analysis, and control of dynamical systems can be brought to an optimization problem with matrix variable subjected to the s…
Symplectic eigenvalues of positive-semidefinite matrices and the trace minimization theorem
Nguyen Thanh Son, Tatjana Stykel
Symplectic eigenvalues are conventionally defined for symmetric positive-definite matrices via Williamson's diagonal form. Many properties of standard eigenvalues, including the tr…
Symplectic eigenvalue problem via trace minimization and Riemannian optimization
Nguyen Thanh Son, P. -A. Absil, Bin Gao +1
We address the problem of computing the smallest symplectic eigenvalues and the corresponding eigenvectors of symmetric positive-definite matrices in the sense of Williamson's theo…
Riemannian Optimization on the Symplectic Stiefel Manifold
Bin Gao, Nguyen Thanh Son, P. -A. Absil +1
The symplectic Stiefel manifold, denoted by , is the set of linear symplectic maps between the standard symplectic spaces and $\mathbb{R}^{2n}…