A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity

@article{Malitsky2020AFS,
  title={A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity},
  author={Yura Malitsky and Matthew K. Tam},
  journal={SIAM J. Optim.},
  year={2020},
  volume={30},
  pages={1451-1472}
}
In this work, we propose a simple modification of the forward-backward splitting method for finding a zero in the sum of two monotone operators. Our method converges under the same assumptions as Tseng's forward-backward-forward method, namely, it does not require cocoercivity of the single-valued operator. Moreover, each iteration only requires one forward evaluation rather than two as is the case for Tseng's method. Variants of the method incorporating a linesearch, relaxation and inertia, or… 

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