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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年11月19日

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  • Balendu Bhooshan Upadhyay,
  • Jen-Chih Yao,
  • Subham Poddar,
  • Xiaopeng Zhao

摘要

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.