The Proximal Point Algorithm for Monotone Vector Fields on Complete Geodesic Spaces

Authors

  • Shuta Sudo Department of Information Science, Toho University, Miyama, Funabashi, Chiba 274-8510, Japan

DOI:

https://doi.org/10.58715/ncao.2025.4.1

Keywords:

Geodesic space, Monotone vector field, Proximal point algorithm, Zero point approximation

Abstract

In this paper, we deal with monotone vector fields defined on geodesic spaces and their zero point approximation method. In an appropriate setting, we can define the resolvent operator for a given monotone vector field, and then that operator has many useful properties which are effective for the fixed point theory. We will show an approximation theorem for a monotone vector field with the canonical proximal point algorithm.

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Published

2025-05-01

How to Cite

Sudo, S. (2025). The Proximal Point Algorithm for Monotone Vector Fields on Complete Geodesic Spaces. Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications, 4(1), 1–15. https://doi.org/10.58715/ncao.2025.4.1

Issue

Vol. 4 No. 1 (2025): January - June, 2025

Section

Articles

License

Copyright (c) 2025 Shuta Sudo

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