Monotone polygon

Gene

Linguistics

Philosophy

Social psychology

Monotonic function

Zero (linguistics)

Applied mathematics

Biochemistry

Mathematical optimization

Simple (philosophy)

Classical mechanics

Operator splitting

Physics

Psychology

Mathematics

Relaxation (psychology)

Epistemology

Transcription factor

Mathematical analysis

Inertia

Geometry

Repressor

Chemistry

Operator (biology)

SIAM Journal on Optimization

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 uses 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.

A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity