# The method of Bregman projections in deterministic and stochastic convex feasibility problems

arXiv: https://arxiv.org/abs/2101.01704 · HTML: https://mlsanity.com/paper/2101.01704/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2021.

## Built on by (most cited first, 1 of 1)

- [Convergence of Batch Greenkhorn for Regularized Multimarginal Optimal Transport](https://mlsanity.com/paper/2112.00838/) (2021)

## Abstract (arXiv)

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.