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Spectral projected subgradient method with a 1-memory momentum term for constrained multiobjective optimization problem

Author

Listed:
  • Jing-jing Wang

    (Sichuan University)

  • Li-ping Tang

    (Chongqing Normal University)

  • Xin-min Yang

    (Chongqing Normal University)

Abstract

In this paper, we propose a spectral projected subgradient method with a 1-memory momentum term for solving constrained convex multiobjective optimization problem. This method combines the subgradient-type algorithm for multiobjective optimization problems with the idea of the spectral projected algorithm to accelerate the convergence process. Additionally, a 1-memory momentum term is added to the subgradient direction in the early iterations. The 1-memory momentum term incorporates, in the present iteration, some of the influence of the past iterations, and this can help to improve the search direction. Under suitable assumptions, we show that the sequence generated by the method converges to a weakly Pareto efficient solution and derive the sublinear convergence rates for the proposed method. Finally, computational experiments are given to demonstrate the effectiveness of the proposed method.

Suggested Citation

  • Jing-jing Wang & Li-ping Tang & Xin-min Yang, 2024. "Spectral projected subgradient method with a 1-memory momentum term for constrained multiobjective optimization problem," Journal of Global Optimization, Springer, vol. 89(2), pages 277-302, June.
    • Handle: RePEc:spr:jglopt:v:89:y:2024:i:2:d:10.1007_s10898-023-01349-x
    DOI: 10.1007/s10898-023-01349-x
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    References listed on IDEAS

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    1. Birgin, Ernesto G. & Martínez, Jose Mario & Raydan, Marcos, 2014. "Spectral Projected Gradient Methods: Review and Perspectives," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i03).
    2. Xiaopeng Zhao & Jen-Chih Yao, 2022. "Linear convergence of a nonmonotone projected gradient method for multiobjective optimization," Journal of Global Optimization, Springer, vol. 82(3), pages 577-594, March.
    3. White, D.J., 1998. "Epsilon-dominating solutions in mean-variance portfolio analysis," European Journal of Operational Research, Elsevier, vol. 105(3), pages 457-466, March.
    4. Chen, Wang & Yang, Xinmin & Zhao, Yong, 2023. "Memory gradient method for multiobjective optimization," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    5. Ralph E. Steuer & Yue Qi & Markus Hirschberger, 2008. "Portfolio Selection in the Presence of Multiple Criteria," Springer Optimization and Its Applications, in: Constantin Zopounidis & Michael Doumpos & Panos M. Pardalos (ed.), Handbook of Financial Engineering, pages 3-24, Springer.
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