Strong convergence of inertial forward–backward methods for solving monotone inclusions

ABSTRACT

The paper presents four modifications of the inertial forward–backward splitting method for monotone inclusion problems in the framework of real Hilbert spaces. The advantages of our iterative schemes are that the single-valued operator is Lipschitz continuous monotone rather than cocoercive and the Lipschitz constant does not require to be known. The strong convergence of the suggested approaches is obtained under some standard and mild conditions. Finally, several numerical experiments in finite- and infinite-dimensional spaces are proposed to demonstrate the advantages of our algorithms over the existing related ones.

Keywords:

• Inclusion problem
• inertial forward–backward method
• projection and contraction method
• Tseng's splitting method
• viscosity method

Mathematics Subject Classifications:

• 47H05
• 47J22
• 47J25
• 68W10
• 65K15

Acknowledgements

The authors are very grateful to the anonymous referees for their constructive comments, which significantly improved the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).