A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity

Understand

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.