On the linear convergence rate of a relaxed forward–backward splitting method

ABSTRACT

We focus on a relaxed version of the classic forward–backward splitting method in the context of finding a zero point of the sum of two monotone operators, and derive its linear convergence rate. The proof is very short by using the recently proposed concept of negatively averaged operator.

Keywords:

• Forward–backward splitting method
• linear convergence rate
• monotone operator
• negatively averaged operator

2010 Mathematics Subject Classifications:

• 90C25
• 65K15
• 47H05
• 47J20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This author was supported by the Natural Science Foundation of China [grant numbers 11801455, 11971238], China Postdoctoral Science Foundation [grant number 2019M663459], the Applied Basic Project of Sichuan Province [grant number 20YYJC2523], Fundamental Research Funds of China West Normal University [grant numbers 17E084, 18B031].