BDRS Can Fail for Matrix Scaling and Optimal Transport
We show that the Bregman Douglas–Rachford splitting method (BDRS) can fail for matrix scaling and unregularized optimal transport. For matrix scaling, we construct a strictly positive \(36\times6\) integer matrix, positive rational marginals of equal mass, and a positive auxiliary initialization for which the matrix iterates enter a nonconstant six-cycle after one iteration. The construction prescribes … Read more