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A Trust Region Method for Solving Multicriteria Optimization Problems on Riemannian Manifolds

Author

Listed:
  • N. Eslami

    (Amirkabir University of Technology (Tehran Polytechnic))

  • B. Najafi

    (Amirkabir University of Technology (Tehran Polytechnic))

  • S. M. Vaezpour

    (Amirkabir University of Technology (Tehran Polytechnic))

Abstract

We extend and analyze the trust region method for solving smooth and unconstrained multicriteria optimization problems on Riemannian manifolds. At each iteration of this method, a quadratic model is assigned to each component of the vectorial objective function by considering the notion of retractions. Then, a subproblem is constructed and solved to find a new descent direction. Furthermore, we investigate the convergence behavior of the algorithm by considering radially Lipschitz continuously differentiable functions. In the end, the algorithm is implemented on three examples, and the corresponding numerical results showing the efficiency of the proposed method are reported as well.

Suggested Citation

  • N. Eslami & B. Najafi & S. M. Vaezpour, 2023. "A Trust Region Method for Solving Multicriteria Optimization Problems on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 212-239, January.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:1:d:10.1007_s10957-022-02142-8
    DOI: 10.1007/s10957-022-02142-8
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    References listed on IDEAS

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    1. Kely D. V. Villacorta & Paulo R. Oliveira & Antoine Soubeyran, 2014. "A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 865-889, March.
    2. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, June.
    3. Glaydston de C. Bento & João Xavier Cruz Neto & Lucas V. Meireles, 2018. "Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization of Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 37-52, October.
    4. Orizon P. Ferreira & Mauricio S. Louzeiro & Leandro F. Prudente, 2020. "Iteration-Complexity and Asymptotic Analysis of Steepest Descent Method for Multiobjective Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 507-533, February.
    5. G. C. Bento & J. X. Cruz Neto, 2013. "A Subgradient Method for Multiobjective Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 125-137, October.
    6. G. C. Bento & O. P. Ferreira & P. R. Oliveira, 2012. "Unconstrained Steepest Descent Method for Multicriteria Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 88-107, July.
    7. G. C. Bento & J. X. Cruz Neto & P. S. M. Santos, 2013. "An Inexact Steepest Descent Method for Multicriteria Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 108-124, October.
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    Cited by:

    1. Shahabeddin Najafi & Masoud Hajarian, 2023. "Multiobjective Conjugate Gradient Methods on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1229-1248, June.

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