Separable self-concordant spectral functions and a conjecture of Tunçel
The authors show that the associated spectral function \[ F(X)= (f\circ\lambda)(X) \] for a given separable strongly self-concordant function \(f: \mathbb{R}^n\to\mathbb{R}\) is also a strongly self-concordant function. In addition, there is a universal constant \(O\leq 22\) such that if \(f(x)\) is a separable self-concordant barrier, then \(OF(X)\) is a self-concordant barrier. This generalizes the relationship between the \[ -\sum^n_{i=1}\log x_i\text{ and }\log\text{det\,}X \] and gives a partial solution to a conjecture of Tunçel.
scientific article; zbMATH DE number 5799374