# Asymmetric Forward-Backward-Adjoint Splitting for Solving Monotone Inclusions Involving Three Operators

arXiv: https://arxiv.org/abs/1602.08729 · HTML: https://mlsanity.com/paper/1602.08729/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2016.

## Built on by (most cited first, 8 of 8)

- [Solving stochastic weak Minty variational inequalities without increasing batch size](https://mlsanity.com/paper/2302.09029/) (2023)
- [Escaping limit cycles: Global convergence for constrained nonconvex-nonconcave minimax problems](https://mlsanity.com/paper/2302.09831/) (2023)
- [Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradient](https://mlsanity.com/paper/2301.04431/) (2023)
- [DISA: A Dual Inexact Splitting Algorithm for Distributed Convex Composite Optimization](https://mlsanity.com/paper/2209.01850/) (2022)
- [Decentralized Inexact Proximal Gradient Method With Network-Independent Stepsizes for Convex Composite Optimization](https://mlsanity.com/paper/2302.03238/) (2023)
- [Convergence of the Chambolle-Pock Algorithm in the Absence of Monotonicity](https://mlsanity.com/paper/2312.06540/) (2023)
- [BALPA: A Balanced Primal-Dual Algorithm for Nonsmooth Optimization with Application to Distributed Optimization](https://mlsanity.com/paper/2212.02835/) (2022)
- [Stability of Primal-Dual Gradient Flow Dynamics for Multi-Block Convex Optimization Problems](https://mlsanity.com/paper/2408.15969/) (2024)

## Abstract (arXiv)

In this work we propose a new splitting technique, namely Asymmetric Forward-Backward-Adjoint splitting, for solving monotone inclusions involving three terms, a maximally monotone, a cocoercive and a bounded linear operator. Classical operator splitting methods, like Douglas-Rachford and Forward-Backward splitting are special cases of our new algorithm. Asymmetric Forward-Backward-Adjoint splitting unifies, extends and sheds light on the connections between many seemingly unrelated primal-dual algorithms for solving structured convex optimization problems proposed in recent years. More importantly, it greatly extends the scope and applicability of splitting techniques to a wider variety of problems. One important special case leads to a Douglas-Rachford type scheme that includes a third cocoercive operator.