Dykstras algorithm with bregman projections: A convergence proof

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Construction of best Bregman approximations in reflexive Banach spaces (2003, methodology): “Furthermore, the methods of [4, 7, 11] demand the ability to perform D-projections onto each Si.”
Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces (2006, unknown): “nonlinear mappings and more (see [23], [24], [27], [40], [48], [49], [51], [65], [3], [6], [12], [ 16 ], [20], [26], [29], [28], [33], [36], [59], and the references therein).”
Dykstra's Algorithm, ADMM, and Coordinate Descent: Connections, Insights, and Extensions (2017, background): “As shown in Censor and Reich (1998); Bauschke and Lewis (2000), Dykstra’s algorithm can be extended to apply to (18).”
Belief Propagation, Dykstra's Algorithm, and Iterated Information Projections (2010, methodology): “Further developments of interest have been developed by Bauschke and co-workers [43], [ 36 ], [41], who extended both the class of algorithms to which such iterative procedures apply and the class of functionals to be used as divergence measures.”
Scaling Algorithms for Unbalanced Transport Problems (2016, methodology): “Dykstra’s algorithm is known to converge when used in conjunction with Bregman divergences [5, 22] (see [58] for details on the underlying idea for sums of two arbitrary functions).”
Applied Iterative Methods (2007, background): “For further details, see the papers of Censor and Reich [57] and Bauschke and Lewis [12].”