mlsanityData to 7 Oct 2026

A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity

arXiv 1808.04162 ↗First posted 13 Aug 2018math.OCcited by 35

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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.

Key facts. Cited by 35 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Aug 2018.

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Citing papers per year: 2021: 2; 2022: 10; 2023: 8; 2024: 6; 2025: 4; 2026: 5.

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  1. 2021Stochastic Variance Reduction for Variational Inequality Methodscited by 46
  2. 2022Stochastic Gradient Descent-Ascent: Unified Theory and New Efficient Methodscited by 37
  3. 2022Accelerated Single-Call Methods for Constrained Min-Max Optimizationcited by 31
  4. 2022Proximal Point Imitation Learningcited by 25
  5. 2023Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradientcited by 19
  6. 2023ReLOAD: Reinforcement Learning with Optimistic Ascent-Descent for Last-Iterate Convergence in Constrained MDPscited by 19
  7. 2022Generalized Optimistic Methods for Convex-Concave Saddle Point Problemscited by 15
  8. 2022Beyond the Golden Ratio for Variational Inequality Algorithmscited by 12
  9. 2022Smooth Monotone Stochastic Variational Inequalities and Saddle Point Problems: A Surveycited by 10
  10. 2023Variance Reduced Halpern Iteration for Finite-Sum Monotone Inclusionscited by 10
  11. 2023Randomized Block-Coordinate Optimistic Gradient Algorithms for Root-Finding Problemscited by 9
  12. 2024Adaptive and Optimal Second-order Optimistic Methods for Minimax Optimizationcited by 8
23 more
  1. 2022Accelerated first-order methods for convex optimization with locally Lipschitz continuous gradientcited by 5
  2. 2022Differentiating Nonsmooth Solutions to Parametric Monotone Inclusion Problemscited by 5
  3. 2023Sublinear Convergence Rates of Extragradient-Type Methods: A Survey on Classical and Recent Developmentscited by 5
  4. 2024Revisiting Inexact Fixed-Point Iterations for Min-Max Problems: Stochasticity and Structured Nonconvexitycited by 4
  5. 2025Nesterov Finds GRAAL: Optimal and Adaptive Gradient Method for Convex Optimizationcited by 4
  6. 2022Distributed saddle point problems for strongly concave-convex functionscited by 3
  7. 2024Functional Acceleration for Policy Mirror Descentcited by 3
  8. 2025Multi-Step Alignment as Markov Games: An Optimistic Online Gradient Descent Approach with Convergence Guaranteescited by 3
  9. 2024Diffusion Stochastic Optimization for Min-Max Problemscited by 2
  10. 2024An Inexact Halpern Iteration with Application to Distributionally Robust Optimizationcited by 2
  11. 2026Unbiased and Biased Variance-Reduced Forward-Reflected-Backward Splitting Methods for Stochastic Composite Inclusionscited by 2
  12. 2021Stochastic Projective Splitting: Solving Saddle-Point Problems with Multiple Regularizerscited by 1
  13. 2022Primal-dual extrapolation methods for monotone inclusions under local Lipschitz continuitycited by 1
  14. 2023Extragradient Type Methods for Riemannian Variational Inequality Problemscited by 1
  15. 2025Nonconvex Regularization for Feature Selection in Reinforcement Learningcited by 1
  16. 2026How to Make the Gradient Mapping Small for Constrained Stochastic Min-Max Problems and Beyondcited by 1
  17. 2023Extragradient-Type Methods with O (1/k) Last-Iterate Convergence Rates for Co-Hypomonotone Inclusionscited by 0
  18. 2023An Augmented Lagrangian Approach to Conically Constrained Non-monotone Variational Inequality Problemscited by 0
  19. 2024Near-Optimal Distributed Minimax Optimization under the Second-Order Similaritycited by 0
  20. 2025Shuffling Heuristic in Variational Inequalities: Establishing New Convergence Guaranteescited by 0
  21. 2026Mirror Descent-Type Algorithms for the Variational Inequality Problem with Functional Constraintscited by 0
  22. 2026Non-Convex Sparse Reinforcement Learning via Non-Monotone Inclusionscited by 0
  23. 2026Provable Parameter-Free Fixed-Point Algorithms with Linear Convergence Ratescited by 0