Asynchronous block-iterative primal-dual decomposition methods for monotone inclusions

@article{Combettes2018AsynchronousBP,
  title={Asynchronous block-iterative primal-dual decomposition methods for monotone inclusions},
  author={Patrick L. Combettes and Jonathan Eckstein},
  journal={Mathematical Programming},
  year={2018},
  volume={168},
  pages={645-672}
}
We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the sense that, at each iteration, only a subset of the monotone operators needs to be processed, as opposed to all operators as in established methods. Flexible strategies are used to select the blocks of operators activated at each iteration. In addition, we allow… 
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