A viscosity-type scheme for optimization problems in Hadamard spaces with applications

Abstract

In this article, we propose a viscosity-type scheme for approximating a common solution of convex minimization problem, monotone vector field inclusion problem and fixed point problem involving multi-valued nonexpansive mapping in the framework of Hadamard spaces. We obtain a strong convergence theorem for the sequence generated therefrom to a solution of the problem. Furthermore, we apply our results to compute the Fréchet mean, find the mean of probabilities, minimize energy of measurable mappings and solve a problem of two-arm robotic motion control. Finally, we give numerical example to demonstrate the applicability of the method and also issue comparisons with some existing methods. Our results extend and complement some recent results in the literature.

Keywords:

• Convergence
• fixed point
• Hadamard space
• monotone inclusion
• nonexpansive
• proximal point algorithm

2020 Mathematics Subject Classifications:

• 47H05
• 47J25
• 49J40
• 49M30
• 65K10
• 65K15

Acknowledgments

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 2023 under project number FRB660073/0164.

Disclosure statement

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

Additional information

Funding

This research was funded by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2022 under project number FRB650048/0164. The first author was supported by the ‘Petchra Pra Jom Klao Ph.D. Research Scholarship’ from ‘King Mongkut's University of Technology Thonburi’ with the number 67/2563.