Shadow Douglas–Rachford Splitting for Monotone Inclusions

@article{Csetnek2019ShadowDS,
  title={Shadow Douglas–Rachford Splitting for Monotone Inclusions},
  author={Ern{\"o} Robert Csetnek and Yura Malitsky and Matthew K. Tam},
  journal={Applied Mathematics \& Optimization},
  year={2019},
  volume={80},
  pages={665 - 678}
}
In this work, we propose a new algorithm for finding a zero of the sum of two monotone operators where one is assumed to be single-valued and Lipschitz continuous. This algorithm naturally arises from a non-standard discretization of a continuous dynamical system associated with the Douglas–Rachford splitting algorithm. More precisely, it is obtained by performing an explicit, rather than implicit, discretization with respect to one of the operators involved. Each iteration of the proposed… 

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