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Nonmonotone Proximal Gradient Method for Composite Multiobjective Optimization Problems

Author

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  • Jian-Wen Peng

    (Chongqing Normal University)

  • Hua Sun

    (Chongqing Normal University)

  • Elisabeth Köbis

    (Norwegian University of Science and Technology)

Abstract

In this paper, we introduce proximal gradient methods with non-monotone Armijo line search rule of both kinds, max-type and average-type, to solve composite multiobjective optimization problems (CMOP). Moreover, the convergence analysis is given, and we show that all accumulation points of a sequence generated by both of the two kinds of nonmonotone proximal gradient methods are Pareto stationary points of (CMOP). Finally, we present numerical experiments illustrating the practical performance of these methods

Suggested Citation

  • Jian-Wen Peng & Hua Sun & Elisabeth Köbis, 2025. "Nonmonotone Proximal Gradient Method for Composite Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 205(3), pages 1-28, June.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:3:d:10.1007_s10957-025-02667-8
    DOI: 10.1007/s10957-025-02667-8
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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.
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