# A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity

arXiv: https://arxiv.org/abs/1808.04162 · HTML: https://mlsanity.com/paper/1808.04162/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2018.

## Built on by (most cited first, 30 of 36)

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- [Unbiased and Biased Variance-Reduced Forward-Reflected-Backward Splitting Methods for Stochastic Composite Inclusions](https://mlsanity.com/paper/2603.15576/) (2026)
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- [Stochastic Projective Splitting: Solving Saddle-Point Problems with Multiple Regularizers](https://mlsanity.com/paper/2106.13067/) (2021)
- [Primal-dual extrapolation methods for monotone inclusions under local Lipschitz continuity](https://mlsanity.com/paper/2206.00973/) (2022)
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- [Extragradient-Type Methods with O (1/k) Last-Iterate Convergence Rates for Co-Hypomonotone Inclusions](https://mlsanity.com/paper/2302.04099/) (2023)
- [An Augmented Lagrangian Approach to Conically Constrained Non-monotone Variational Inequality Problems](https://mlsanity.com/paper/2306.01214/) (2023)

## Abstract (arXiv)

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 a structured three operator inclusion are also discussed.