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Adaptive Generalized Conditional Gradient Method for Multiobjective Optimization

Author

Listed:
  • Anteneh Getachew Gebrie

    (Perimeter Institute for Theoretical Physics
    Kyoto University)

  • Ellen Hidemi Fukuda

    (Kyoto University)

Abstract

In this paper, we propose a generalized conditional gradient method for multiobjective optimization, where the objective function is the sum of a smooth function and a possibly nonsmooth function. The proposed method is an improved extension of the classical Frank-Wolfe method of single-objective optimization to the multiobjective optimization problem. The method combines the so-called normalized descent direction as an adaptive procedure and the line search technique. We prove the convergence of the algorithm with respect to Pareto optimality under mild assumptions. The iteration complexity for obtaining an approximate Pareto critical point and the convergence rate in terms of a merit function is also analyzed. Finally, we report some numerical results, which demonstrate the feasibility and competitiveness of the proposed method.

Suggested Citation

  • Anteneh Getachew Gebrie & Ellen Hidemi Fukuda, 2025. "Adaptive Generalized Conditional Gradient Method for Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 206(1), pages 1-27, July.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:1:d:10.1007_s10957-025-02691-8
    DOI: 10.1007/s10957-025-02691-8
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    References listed on IDEAS

    as
    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. G. Cocchi & G. Liuzzi & S. Lucidi & M. Sciandrone, 2020. "On the convergence of steepest descent methods for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 77(1), pages 1-27, September.
    4. Z. R. Gabidullina, 2019. "Adaptive Conditional Gradient Method," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 1077-1098, December.
    5. G. Cocchi & G. Liuzzi & A. Papini & M. Sciandrone, 2018. "An implicit filtering algorithm for derivative-free multiobjective optimization with box constraints," Computational Optimization and Applications, Springer, vol. 69(2), pages 267-296, March.
    6. Marguerite Frank & Philip Wolfe, 1956. "An algorithm for quadratic programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 95-110, March.
    7. Madani Bezoui & Mustapha Moulaï & Ahcène Bounceur & Reinhardt Euler, 2019. "An iterative method for solving a bi-objective constrained portfolio optimization problem," Computational Optimization and Applications, Springer, vol. 72(2), pages 479-498, March.
    8. 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.
    9. Mustapha El Moudden & Ahmed El Ghali, 2018. "A new reduced gradient method for solving linearly constrained multiobjective optimization problems," Computational Optimization and Applications, Springer, vol. 71(3), pages 719-741, December.
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