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Recently, Sinkhornu0027s algorithm was applied for approximately solving linear programs emerging from optimal transport very effeciently [M. Cuturi, Advances in Neural Information Processing Systems, 2013, pp. 2292--2300]. This was accomplished by formulating a regularized version of the linear program as a Bregman projection problem onto the polytope of doubly stochastic matrices and then computing the projection using the effecient Sinkhorn algorithm, which is based on alternating closed-form Bregman projections on the larger polytopes of row-stochastic and column-stochastic matrices. In this paper we suggest a generalization of this algorithm for solving a well-known lifted linear program relaxations of the quadratic assignment problem, which is known as the Johnson--Adams (JA) relaxation. First, an effecient algorithm for Bregman projection onto the JA polytope by alternating closed-form Bregman projections onto one-sided local polytopes is devised. The one-sided polytopes can be seen as a high-dimension...

Sinkhorn Algorithm for Lifted Assignment Problems