Self-Concordance and Matrix Monotonicity with Applications to Quantum Entanglement Problems

Let $V$ be an Euclidean Jordan algebra and $\Omega$ be a cone of invertible squares in $V$. Suppose that $g:\mathbb{R}_{+} \to \mathbb{R}$ is a matrix monotone function on the positive semiaxis which naturally induces a function $\tilde{g}: \Omega \to V$. We show that $-\tilde{g}$ is compatible (in the sense of Nesterov-Nemirovski) with the standard self-concordant … Read more