  In this work we study the method of Bregman projections for deterministic and
stochastic convex feasibility problems with three types of control sequences
for the selection of sets during the algorithmic procedure: greedy, random, and
adaptive random. We analyze in depth the case of affine feasibility problems
showing that the iterates generated by the proposed methods converge Q-linearly
and providing also explicit global and local rates of convergence. This work
generalizes from one hand recent developments in randomized methods for the
solution of linear systems based on orthogonal projection methods. On the other
hand, our results yield global and local Q-linear rates of convergence for the
Sinkhorn and Greenhorn algorithms in discrete entropic-regularized optimal
transport, for the first time, even in the multimarginal setting.
