T. Le

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20172026

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math.OC2020

Simultaneous diagonalization via congruence of $m$ real symmetric matrices and its implications in optimization

Thi-Ngan Nguyen, Van-Bong Nguyen, Thanh-Hieu Le +1

Let ${C_{1}, C_{2}, \dots, C_{m}}, m \geq 2$ be a collection of $n \times n$ real symmetric matrices. The objective of the paper is to offer an algorithm that finds a common congruence ma…

math.OC2019

Sum-of-square-of-rational-function based representations of positive semidefinite polynomial matrices

Thanh-Hieu Le, Nhat-Thien Pham

The paper proves sum-of-square-of-rational-function based representations (shortly, sosrf-based representations) of polynomial matrices that are positive semidefinite on some speci…

math.OC2017

Low rank solutions to differentiable systems over matrices and applications

Thanh Hieu Le

Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for fin…

Simultaneous diagonalization via congruence of m real symmetric matrices and its implications in optimization

Sum-of-square-of-rational-function based representations of positive semidefinite polynomial matrices

Low rank solutions to differentiable systems over matrices and applications

Simultaneous diagonalization via congruence of $m$ real symmetric matrices and its implications in optimization