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Semivectorial Bilevel Optimization on Riemannian Manifolds

Author

Listed:
  • Henri Bonnel

    (Université de la Nouvelle-Calédonie)

  • Léonard Todjihoundé

    (Institut de Mathématiques et de Sciences Physiques)

  • Constantin Udrişte

    (University Politehnica of Bucharest)

Abstract

In this paper, we deal with the semivectorial bilevel problem in the Riemannian setting. The upper level is a scalar optimization problem to be solved by the leader, and the lower level is a multiobjective optimization problem to be solved by several followers acting in a cooperative way inside the greatest coalition and choosing among Pareto solutions with respect to a given ordering cone. For the so-called optimistic problem, when the followers choice among their best responses is the most favorable for the leader, we give optimality conditions. Also for the so-called pessimistic problem, when there is no cooperation between the leader and the followers, and the followers choice may be the worst for the leader, we present an existence result.

Suggested Citation

  • Henri Bonnel & Léonard Todjihoundé & Constantin Udrişte, 2015. "Semivectorial Bilevel Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 464-486, November.
  • Handle: RePEc:spr:joptap:v:167:y:2015:i:2:d:10.1007_s10957-015-0789-6
    DOI: 10.1007/s10957-015-0789-6
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    References listed on IDEAS

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    9. Henri Bonnel & Julien Collonge, 2014. "Stochastic Optimization over a Pareto Set Associated with a Stochastic Multi-Objective Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 405-427, August.
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    Cited by:

    1. Henri Bonnel & Christopher Schneider, 2019. "Post-Pareto Analysis and a New Algorithm for the Optimal Parameter Tuning of the Elastic Net," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 993-1027, December.
    2. Peng Zhang & Gejun Bao, 2018. "An Incremental Subgradient Method on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 711-727, March.

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