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An away-step Frank–Wolfe algorithm for constrained multiobjective optimization

Author

Listed:
  • Douglas S. Gonçalves

    (Universidade Federal de Santa Catarina)

  • Max L. N. Gonçalves

    (IME, Universidade Federal de Goiás)

  • Jefferson G. Melo

    (IME, Universidade Federal de Goiás)

Abstract

In this paper, we propose and analyze an away-step Frank–Wolfe algorithm designed for solving multiobjective optimization problems over polytopes. We prove that each limit point of the sequence generated by the algorithm is a weak Pareto optimal solution. Furthermore, under additional conditions, we show linear convergence of the whole sequence to a Pareto optimal solution. Numerical examples illustrate a promising performance of the proposed algorithm in problems where the multiobjective Frank–Wolfe convergence rate is only sublinear.

Suggested Citation

  • Douglas S. Gonçalves & Max L. N. Gonçalves & Jefferson G. Melo, 2024. "An away-step Frank–Wolfe algorithm for constrained multiobjective optimization," Computational Optimization and Applications, Springer, vol. 88(3), pages 759-781, July.
    • Handle: RePEc:spr:coopap:v:88:y:2024:i:3:d:10.1007_s10589-024-00577-5
    DOI: 10.1007/s10589-024-00577-5
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    References listed on IDEAS

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    1. Hiroki Tanabe & Ellen H. Fukuda & Nobuo Yamashita, 2019. "Proximal gradient methods for multiobjective optimization and their applications," Computational Optimization and Applications, Springer, vol. 72(2), pages 339-361, March.
    2. Hiroki Tanabe & Ellen H. Fukuda & Nobuo Yamashita, 2023. "An accelerated proximal gradient method for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 86(2), pages 421-455, November.
    3. Wang Chen & Xinmin Yang & Yong Zhao, 2023. "Conditional gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 85(3), pages 857-896, July.
    4. E. Carrizosa & J. B. G. Frenk, 1998. "Dominating Sets for Convex Functions with Some Applications," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 281-295, February.
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