On the Bregman-proximal iterative algorithm for the monotone inclusion problem in Banach spaces

Abstract

In this paper, we focus on the solution of a class of monotone inclusion problems in reflexive Banach spaces. To reflect the geometry of the space and the operator, a more general proximal point iterative algorithm with Bregman divergence is proposed and some strong convergence results for the proposed scheme under standard assumptions are obtained. Meanwhile, the convex optimization problems and the critical point problems are studied in the applications, and the recovery of the sparse signal is simulated in the numerical experiments.

Keywords:

• Bregman divergence
• monotone inclusion
• proximal point algorithm
• reflexive Banach spaces

2000 Mathematics Subject Classification:

• 65K05
• 65K10
• 47H10
• 47L25

Authors’ contributions

All authors contributed equally to this work. All authors read and approved the final manuscript.

Disclosure statement

The authors declare that they have no competing interests.

Data availability statement

All data generated or analyzed during this study are included in this published article.

Additional information

Funding

This article was funded by the National Natural Science Foundation of China (12071316), the Natural Science Foundation of Chongqing (cstc2021jcyj-msxmX0177), the Team Building Project for Graduate Tutors in Chongqing (yds223010).