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An augmented subgradient method for minimizing nonsmooth DC functions

Author

Listed:
  • A. M. Bagirov

    (Federation University Australia)

  • N. Hoseini Monjezi

    (University of Isfahan)

  • S. Taheri

    (RMIT University)

Abstract

A method, called an augmented subgradient method, is developed to solve unconstrained nonsmooth difference of convex (DC) optimization problems. At each iteration of this method search directions are found by using several subgradients of the first DC component and one subgradient of the second DC component of the objective function. The developed method applies an Armijo-type line search procedure to find the next iteration point. It is proved that the sequence of points generated by the method converges to a critical point of the unconstrained DC optimization problem. The performance of the method is demonstrated using academic test problems with nonsmooth DC objective functions and its performance is compared with that of two general nonsmooth optimization solvers and five solvers specifically designed for unconstrained DC optimization. Computational results show that the developed method is efficient and robust for solving nonsmooth DC optimization problems.

Suggested Citation

  • A. M. Bagirov & N. Hoseini Monjezi & S. Taheri, 2021. "An augmented subgradient method for minimizing nonsmooth DC functions," Computational Optimization and Applications, Springer, vol. 80(2), pages 411-438, November.
    • Handle: RePEc:spr:coopap:v:80:y:2021:i:2:d:10.1007_s10589-021-00304-4
    DOI: 10.1007/s10589-021-00304-4
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    References listed on IDEAS

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    9. Kaisa Joki & Adil M. Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2017. "A proximal bundle method for nonsmooth DC optimization utilizing nonconvex cutting planes," Journal of Global Optimization, Springer, vol. 68(3), pages 501-535, July.
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