Resolvent splitting for sums of monotone operators with minimal lifting

@article{Malitsky2021ResolventSF,
  title={Resolvent splitting for sums of monotone operators with minimal lifting},
  author={Yura Malitsky and Matthew K. Tam},
  journal={Mathematical Programming},
  year={2021}
}
In this work, we study fixed point algorithms for finding a zero in the sum of n ≥ 2 maximally monotone operators by using their resolvents. More precisely, we consider the class of such algorithms where each resolvent is evaluated only once per iteration. For any algorithm from this class, we show that the underlying fixed point operator is necessarily defined on a d -fold Cartesian product space with d ≥ n − 1. Further, we show that this bound is unimprovable by providing a family of examples for… 
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