Conequences of using barrier for quantum relative entropy not known to be self-concordant?

[Mark-L-Stone]

Per p. 23 of DOMAIN-DRIVEN SOLVER (DDS) VERSION 2.0: A MATLAB-BASED SOFTWARE PACKAGE FOR CONVEX OPTIMIZATION PROBLEMS IN DOMAIN-DRIVEN FORM., MEHDI KARIMI AND LEVENT TUNCEL ,

DDS 2.0 uses the following barrier (not yet known to be s.c.) for solving problems involving quantum relative entropy constraints: Φ(t, X, Y ) := ln(t −qre(X, Y )) −ln det(X) −ln det(Y )

What are the consequences of using a barrier not known to be self-concordant? If the barrier is not actually self-concordant, could that result in an incorrect solution, non-convergence, or something else?

[Mark-L-Stone]

Hamza Fawzi and James Saunderson proved the self-concordance of this barrier in "Optimal self-concordant barriers for quantum relative entropies" https://arxiv.org/abs/2205.04581, which was posted in May/June 2022.

Perhaps the DDS paper should be updated accordingly.