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Multiobjective Conjugate Gradient Methods on Riemannian Manifolds

Author

Listed:
  • Shahabeddin Najafi

    (Shahid Beheshti University)

  • Masoud Hajarian

    (Shahid Beheshti University)

Abstract

In this paper, we present the multiobjective optimization methods of conjugate gradient on Riemannian manifolds. The concepts of optimality and Wolfe conditions, as well as Zoutendijk’s theorem, are redefined in this setting. We show that under some standard assumptions, a sequence generated by these algorithms converges to a critical Pareto point. This is when the step sizes satisfy the multiobjective Wolfe conditions. In particular, we propose the Fletcher–Reeves, Dai–Yuan, Polak–Ribière–Polyak, and Hestenes–Stiefel parameters and further analyze the convergence behavior of the first two methods and test their performance against the steepest descent method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:197:y:2023:i:3:d:10.1007_s10957-023-02224-1
    DOI: 10.1007/s10957-023-02224-1
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    References listed on IDEAS

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