Work

A Bregman regularized proximal point method for solving equilibrium problems on Hadamard manifolds

Year: 2026

Type: article

Abstract: In this paper we develop a Bregman regularized proximal point algorithm for solving monotone equilibrium problems on Hadamard manifolds. It has been shown that the regularization term induced by a Bregman function is, in general, nonconvex on Hadamard manifolds unless the curvature is zero. Nevertheless, we prove that the proposed Bregman regularization scheme does converge to a solution of the equilibrium problem on Hadamard manifolds in the presence of a strong assumption on the convexity of a certain set formed by the regularization term. Moreover, we employ a coercivity condition on the Bregman function which is weaker than those typically assumed in the existing literature on Bregman regularization. Numerical experiments on illustrative examples demonstrate the practical effectiveness of our proposed method.

Source: Rendiconti del Circolo Matematico di Palermo Series 2

DOI: 10.1007/s12215-026-01446-2

Authors: Shikher Sharma, Simeon Reich

Institution: Technion – Israel Institute of Technology

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Technion-Israel Institute of Technology