Inertial proximal point algorithm for variational inclusion in Hadamard manifolds

Abstract

In this paper, we consider the inertial proximal point algorithm for finding a zero point of variational inclusions on Hadamard manifolds. Under suitable conditions, it is proved that the sequence generated by the algorithm converges to an element of the set of zero points of variational inclusion problem. As applications, we utilize our results to study the minimization problem and saddle point problem in the setting of Hadamard manifolds.

Keywords:

• Monotone inclusion problem
• Hadamard manifold
• regularization method
• inertial proximal point algorithm
• Fejér monotone

Subjclass (2010):

• 49J53
• 58E35
• 47J22
• 58C30

Acknowledgements

The authors are grateful to the editor and the referees for their valuable comments and suggestions.

Disclosure statement

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

Additional information

Funding

This work was supported by the Natural Science Foundation of China Medical University, Taiwan; the Scientific Research Fund of Sichuan Provincial Department of Science and Technology [grant number 2018JY0334]; the Scientific Research Fund of SiChuan Provincial Education Department [grant number 14ZA0272].