Proximal Point Method with Bregman Regularization for Multiobjective Optimization Problems on Hadamard Manifolds

Balendu Bhooshan Upadhyay (), Jen-Chih Yao (), Subham Poddar () and Xiaopeng Zhao ()
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Balendu Bhooshan Upadhyay: Indian Institute of Technology Patna, Department of Mathematics
Jen-Chih Yao: China Medical University, Research Center for Interneural Computing
Subham Poddar: Indian Institute of Technology Patna, Department of Mathematics
Xiaopeng Zhao: Tiangong University, School of Mathematical Sciences

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 57, 32 pages

Abstract: Abstract In this paper, the proximal point algorithm with Bregman distance (abbreviated as PPA-BD) is introduced to solve a nonsmooth multiobjective optimization problem on Hadamard manifolds (abbreviated as NMOP-HM). We deduce that every cluster point of any sequence obtained from the PPA-BD is a Pareto critical point of the NMOP-HM. Non-trivial examples on Hadamard manifolds are presented to demonstrate the relevance of the results established in this paper. Furthermore, we perform a numerical experiment on the well-known Hadamard manifold, specifically the Poincaré half-plane, to highlight the effectiveness and competitiveness of the PPA-BD. To the best of our knowledge, the PPA-BD has been developed for the first time to solve the NMOP-HM.

Keywords: Proximal point algorithm; Multiobjective optimization; Hadamard manifolds; Bregman distances; 90C29; 90C30; 65Kxx (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02882-3

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