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

Author

Listed:
  • Balendu Bhooshan Upadhyay

    (Indian Institute of Technology Patna, Department of Mathematics)

  • Jen-Chih Yao

    (China Medical University, Research Center for Interneural Computing
    Academy of Romanian Scientists)

  • Subham Poddar

    (Indian Institute of Technology Patna, Department of Mathematics)

  • Xiaopeng Zhao

    (Tiangong University, School of Mathematical Sciences)

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.

Suggested Citation

  • Balendu Bhooshan Upadhyay & Jen-Chih Yao & Subham Poddar & Xiaopeng Zhao, 2026. "Proximal Point Method with Bregman Regularization for Multiobjective Optimization Problems on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 208(1), pages 1-32, January.
    • Handle: RePEc:spr:joptap:v:208:y:2026:i:1:d:10.1007_s10957-025-02882-3
    DOI: 10.1007/s10957-025-02882-3
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