A Convergence Theorem for a Splitting Method and Its Applications in Geodesic Metric Spaces With Negative Curvature

Mathematical Methods in the Applied Sciences 2026

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Authors: Konrawut Khammahawong, Sakan Termkaew, Premyuda Dechboon, Urairat Deepan
DOI: 10.1002/mma.70529
Cited by: 0
References: 14

Abstract

ABSTRACT In this paper, we study a splitting proximal method for minimizing the sum of convex functions defined on metric spaces with negative curvature. Our approach utilizes the resolvent operator and is tailored to the geometry of such spaces. We establish convergence rate theorems for the proposed splitting method by imposing additional conditions on the objective function. Finally, we apply our results to convex optimization problems arising in convex feasibility problems, the centroid problem, and, in particular, the computation of Karcher means.

Fields of Study & Subjects

Optimization and Variational Analysis Mathematical Inequalities and Applications Geometric Analysis and Curvature Flows

Publication details

Journal / source
Mathematical Methods in the Applied Sciences
Volume
49
Issue
9
Pages
9411–9423
Publication date
29 January 2026
Language
EN