Generalized Halpern-type forward–backward splitting methods for convex minimization problems with application to image restoration problems

ABSTRACT

In this work, our interest is to investigate the monotone inclusion problem in the framework of real Hilbert spaces. For solving the inclusion problem, we propose a composite iteration for approximating a zero of sum of two operators. We prove its strong convergence under some mild conditions. Finally, we provide a number of applications to convex minimization and image restoration problems including numerical experiments to support our main theorem.

KEYWORDS:

• Forward–backward splitting method
• inclusion problem
• convex minimization problem
• monotone operator
• Hilbert spaces

2010 MSC:

• 47H20
• 49M20
• 49M25
• 49M27
• 47J25
• 47H05

Acknowledgements

This work was completed during my visit to Prof. Juan Martínez-Moreno at Faculty of Experimental Science, Department of Mathematics University of Jaén, Spain between 15 June to 15 September 2018.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This project was supported by Petchra Pra Jom Klao Doctoral Academic Scholarship for Ph.D. Program at KMUTT. Moreover, this project was partially supported by the Thailand Research Fund (TRF) and the King Mongkut's University of Technology Thonburi (KMUTT) (KMUTT 55th Anniversary Commemorative Fund) under the TRF Research Scholar Award (grant number RSA6080047).