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Subgradient Method for Nonconvex Nonsmooth Optimization

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Abstract

In this paper, we introduce a new method for solving nonconvex nonsmooth optimization problems. It uses quasisecants, which are subgradients computed in some neighborhood of a point. The proposed method contains simple procedures for finding descent directions and for solving line search subproblems. The convergence of the method is studied and preliminary results of numerical experiments are presented. The comparison of the proposed method with the subgradient and the proximal bundle methods is demonstrated using results of numerical experiments.

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Acknowledgements

The authors would like to thank two anonymous referees for their valuable comments that improved the quality of the paper.

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Authors and Affiliations

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

    A. M. Bagirov, L. Jin, A. Al Nuaimat & N. Sultanova

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

    N. Karmitsa

Authors
  1. A. M. Bagirov
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  2. L. Jin
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  3. N. Karmitsa
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  4. A. Al Nuaimat
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  5. N. Sultanova
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Corresponding author

Correspondence to A. M. Bagirov.

Additional information

Communicated by Xiaoqi Yang.

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Bagirov, A.M., Jin, L., Karmitsa, N. et al. Subgradient Method for Nonconvex Nonsmooth Optimization. J Optim Theory Appl 157, 416–435 (2013). https://doi.org/10.1007/s10957-012-0167-6

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  • DOI: https://doi.org/10.1007/s10957-012-0167-6

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