One step proximal point schemes for monotone vector field inclusion problems

Sani Salisu; Poom Kumam; Songpon Sriwongsa; Sani Salisu; Poom Kumam; Songpon Sriwongsa

doi:10.3934/math.2022412

AIMS Mathematics

2022, Volume 7, Issue 5: 7385-7402. doi: 10.3934/math.2022412

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Research article

One step proximal point schemes for monotone vector field inclusion problems

1.
Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
2.
Department of Mathematics, Faculty of Natural and Applied Sciences, Sule Lamido University Kafin Hausa, P.M.B. 048, Jigawa State, Nigeria
3.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Received: 09 November 2021 Revised: 09 January 2022 Accepted: 17 January 2022 Published: 11 February 2022
MSC : 47H05, 47J25, 49J40, 65K10, 65K15

In this paper, we propose one step convex combination of proximal point algorithms for countable collection of monotone vector fields in CAT(0) spaces. We establish $ \Delta $-convergence and strong convergence theorems for approximating a common solution of a countable family of monotone vector field inclusion problems. Furthermore, we apply our methods to solve a family of minimization problems, compute Frechét mean and geometric median in CAT(0) spaces, and solve a kinematic problem in robotic motion control. Finally, we give a numerical example to show the efficiency and robustness of the proposed scheme in comparison to a known scheme in the literature.
- CAT(0) space,
- monotone vector field,
- proximal point algorithm,
- resolvent operator,
- tangent space,
- $ \Delta $-convergence
Citation: Sani Salisu, Poom Kumam, Songpon Sriwongsa. One step proximal point schemes for monotone vector field inclusion problems[J]. AIMS Mathematics, 2022, 7(5): 7385-7402. doi: 10.3934/math.2022412

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Abstract

In this paper, we propose one step convex combination of proximal point algorithms for countable collection of monotone vector fields in CAT(0) spaces. We establish $ \Delta $-convergence and strong convergence theorems for approximating a common solution of a countable family of monotone vector field inclusion problems. Furthermore, we apply our methods to solve a family of minimization problems, compute Frechét mean and geometric median in CAT(0) spaces, and solve a kinematic problem in robotic motion control. Finally, we give a numerical example to show the efficiency and robustness of the proposed scheme in comparison to a known scheme in the literature.

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