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An inertial alternating minimization with Bregman distance for a class of nonconvex and nonsmooth problems

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Abstract

In this paper, we propose an inertial alternating minimization with Bregman distance (BIAM) for a class of nonconvex nonsmooth optimization problems. Under more general conditions, we analyzed the global convergence of the proposed algorithm. In particular, the analysis of the decline of merit function is simpler than the existing algorithm, and we optimize the parameters selection in the literature. Furthermore, suppose that the merit function satisfies the Kurdyka-Łojasiewicz property and the parameters are selected appropriately, we also prove the convergence of BIAM algorithm. Finally, some preliminary numerical results are reported to illustrate the effectiveness of the algorithm.

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Funding

This work is supported by the National Natural Science Foundation of China (No.12061013, 1160195), Guangxi Natural Science Foundation (2016GXNAFBA380185) and Training Plan of Thousands of Young and Middle-aged Backbone Teachers in Colleges and Universities of Guangxi, and Special Foundation for Guangxi Ba Gui Scholars.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Guangxi University, Nanning, 530004, China

    Miantao Chao, Feifan Nong & Meiyu Zhao

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  1. Miantao Chao
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  2. Feifan Nong
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  3. Meiyu Zhao
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Correspondence to Meiyu Zhao.

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Chao, M., Nong, F. & Zhao, M. An inertial alternating minimization with Bregman distance for a class of nonconvex and nonsmooth problems. J. Appl. Math. Comput. 69, 1559–1581 (2023). https://doi.org/10.1007/s12190-022-01799-8

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