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Aggregate subgradient method for nonsmooth DC optimization

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Abstract

The aggregate subgradient method is developed for solving unconstrained nonsmooth difference of convex (DC) optimization problems. The proposed method shares some similarities with both the subgradient and the bundle methods. Aggregate subgradients are defined as a convex combination of subgradients computed at null steps between two serious steps. At each iteration search directions are found using only two subgradients: the aggregate subgradient and a subgradient computed at the current null step. It is proved that the proposed method converges to a critical point of the DC optimization problem and also that the number of null steps between two serious steps is finite. The new method is tested using some academic test problems and compared with several other nonsmooth DC optimization solvers.

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Notes

  1. We include 148 large test problems since none of four methods succeeded in solving two other problems.

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Acknowledgements

This research by Dr. Adil Bagirov and Dr. Sona Taheri was supported by the Australian Government through the Australian Research Council’s Discovery Projects funding scheme (Project No. DP190100580). The research by Dr. Napsu Karmitsa and Dr. Sona Taheri was supported by the Academy of Finland (Projects Nos. 289500 and 319274).

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Authors and Affiliations

  1. School of Science, Engineering and Information Technology, Federation University Australia, Ballarat, Victoria, Australia

    Adil M. Bagirov & Sona Taheri

  2. Department of Mathematics and Statistics, University of Turku, 20014, Turku, Finland

    Kaisa Joki, Napsu Karmitsa & Marko M. Mäkelä

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  1. Adil M. Bagirov
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  2. Sona Taheri
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  3. Kaisa Joki
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  4. Napsu Karmitsa
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  5. Marko M. Mäkelä
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Correspondence to Sona Taheri.

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Bagirov, A.M., Taheri, S., Joki, K. et al. Aggregate subgradient method for nonsmooth DC optimization. Optim Lett 15, 83–96 (2021). https://doi.org/10.1007/s11590-020-01586-z

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