A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity

Abstract

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.

arXiv comment20 pages, 1 figure

References in corpus (4)

• An inertial forward-backward algorithm for monotone inclusions
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Cited by in corpus (3)

• A Relaxed Inertial Forward-Backward-Forward Algorithm for Solving Monotone Inclusions with Application to GANs
• First-order primal-dual methods for nonsmooth nonconvex optimisation
• Uniqueness of DRS as the 2 Operator Resolvent-Splitting and Impossibility of 3 Operator Resolvent-Splitting