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A class of infeasible proximal bundle methods for nonsmooth nonconvex multi-objective optimization problems

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Abstract

We propose a class of infeasible proximal bundle methods for solving nonsmooth nonconvex multi-objective optimization problems. The proposed algorithms have no requirements on the feasibility of the initial points. In the algorithms, the multi-objective functions are handled directly without any scalarization procedure. To speed up the convergence of the infeasible algorithm, an acceleration technique, i.e., the penalty skill, is applied into the algorithm. The strategies are introduced to adjust the proximal parameters and penalty parameters. Under some wild assumptions, the sequence generated by infeasible proximal bundle methods converges to the globally Pareto solution of multi-objective optimization problems. Numerical results shows the good performance of the proposed algorithms.

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Acknowledgements

The authors thank two anonymous referees for a number of valuable and helpful suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Li-Ping Pang & Jian-Song Yang

  2. Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province, Dalian, 116024, China

    Li-Ping Pang

  3. School of Information and Control Engineering, Qingdao University of Technology, Qingdao, 266520, China

    Fan-Yun Meng

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  1. Li-Ping Pang
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Correspondence to Fan-Yun Meng.

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The research are partially supported by the Na tural Science Foundation of Shandong Province, Grant ZR2019BA014, the Natural Science Foundation of Zhejiang Province, Grant LY20A010025.

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Pang, LP., Meng, FY. & Yang, JS. A class of infeasible proximal bundle methods for nonsmooth nonconvex multi-objective optimization problems. J Glob Optim 85, 891–915 (2023). https://doi.org/10.1007/s10898-022-01242-z

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