Tseng's methods for inclusion problems on Hadamard manifolds

Abstract

In this article, we present two Tseng's methods for finding a singularity point of an inclusion problem which is defined by means of a sum of a single-valued vector field and a multivalued vector field on a Hadamard manifold. Under standard assumptions, we prove any sequence generated by the proposed methods converges to a singularity point, whenever it exists. Moreover, applications to convex minimization problems and variational inequality problems are provided.

Keywords:

• Fixed points
• Hadamard manifolds
• inclusion problems
• maximal monotone vector fields
• monotone vector fields
• Tseng's method

Mathematics Subject Classifications:

• 47H05
• 47J20
• 49J53
• 51H25
• 58A05

Acknowledgments

The authors would like to thank Dr. Wachirapong Jirakitpuwapat and Dr. Habib ur Rehman for a useful discussion. Furthermore, we are grateful to the referee for the valuable suggestions on the paper, which have significantly enhanced it.

Disclosure statement

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

Additional information

Funding

The first author is supported by Postdoctoral Fellowship from King Mongkut's University of Technology Thonburi (KMUTT), Thailand and the third author is supported by KMUTT Research Fund. The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005.