2 problems

Compatibility conjecture. For $\alpha\in[2,\infty)$, the function $-\Psi_\alpha$ is $(\mathbb{H}^n_+,(2\alpha-1)/3)$-compatible with the domain $\mathbb{H}^n_+\times\mathbb{H}^n_+$…

Log trace-inverse self-concordance conjecture. The function $k(X)$ is $(\nu,M)$-generalized self-concordant for some $\nu\in[2,3]$ and $M>0$ on some subset of the positive-definite…