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Trilevel and multilevel optimization using monotone operator theory

Author

Listed:
  • Allahkaram Shafiei

    (Czech Technical University)

  • Vyacheslav Kungurtsev

    (Czech Technical University)

  • Jakub Marecek

    (Czech Technical University)

Abstract

We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term. Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters.

Suggested Citation

  • Allahkaram Shafiei & Vyacheslav Kungurtsev & Jakub Marecek, 2024. "Trilevel and multilevel optimization using monotone operator theory," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 99(1), pages 77-114, April.
    • Handle: RePEc:spr:mathme:v:99:y:2024:i:1:d:10.1007_s00186-024-00852-5
    DOI: 10.1007/s00186-024-00852-5
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    References listed on IDEAS

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    1. Hideaki Iiduka, 2011. "Iterative Algorithm for Solving Triple-Hierarchical Constrained Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 580-592, March.
    2. Lorenzo Lampariello & Christoph Neumann & Jacopo M. Ricci & Simone Sagratella & Oliver Stein, 2020. "An explicit Tikhonov algorithm for nested variational inequalities," Computational Optimization and Applications, Springer, vol. 77(2), pages 335-350, November.
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