Evaluating approximations of the semidefinite cone with trace normalized distance

We evaluate the dual cone of the set of diagonally dominant matrices (resp., scaled diagonally dominant matrices), namely ${\cal DD}_n^*$ (resp., ${\cal SDD}_n^*$), as an approximation of the semidefinite cone. We prove that the norm normalized distance, proposed by Blekherman et al. (2022), between a set ${\cal S}$ and the semidefinite cone has the same … Read more