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20172024
most citedSymplectic eigenvalues of positive-semidefinite matrices and the trace minimization theorem

11 citations · 13 across the 5 of their papers we have counts for

collaborators

10 papers

math.OC2024★ 1 cited

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…

math.OC2024

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…

math.OC2022

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…

math.OC2022★ 11 cited

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…

math.OC2021

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…

math.OC2020

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}…