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Subgradient Smoothing Method for Nonsmooth Nonconvex Optimization

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Numerical Analysis and Optimization (NAO 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 354))

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Abstract

In this chapter an unconstrained nonsmooth nonconvex optimization problem is considered and a method for solving this problem is developed. In this method the subproblem for finding search directions is reduced to the unconstrained minimization of a smooth function. This is achieved by using subgradients computed in some neighborhood of a current iteration point and by formulating the search direction finding problem to the minimization of the convex piecewise linear function over the unit ball. The hyperbolic smoothing technique is applied to approximate the minimization problem by a sequence of smooth problems. The convergence of the proposed method is studied and its performance is evaluated using a set of nonsmooth optimization academic test problems. In addition, the method is implemented in GAMS and numerical results using different solvers from GAMS are reported. The proposed method is compared with a number of nonsmooth optimization methods.

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Acknowledgements

The work is financially supported by the Australian Government through the Australian Research Council’s Discovery Projects funding scheme (Project No. DP19000580) and partially by the Academy of Finland (Project No. 319274).

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Authors and Affiliations

  1. School of Engineering, Information Technology and Physical Sciences, Federation University Australia, Ballarat, Australia

    A. M. Bagirov & N. Sultanova

  2. School of Science, RMIT University, Melbourne, Australia

    S. Taheri

  3. Department of Industrial Engineering, Eskisehir Technical University, Eskisehir, Turkey

    G. Ozturk

Authors
  1. A. M. Bagirov
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  2. N. Sultanova
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  3. S. Taheri
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  4. G. Ozturk
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Corresponding author

Correspondence to A. M. Bagirov .

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Editors and Affiliations

  1. Department of Mathematics, Sultan Qaboos University, Muscat, Oman

    Mehiddin Al-Baali

  2. Department of Mathematics, Sultan Qaboos University, Muscat, Oman

    Anton Purnama

  3. DIMES, University of Calabria, Arcavacada di Rende, Cosenza, Italy

    Lucio Grandinetti

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Bagirov, A.M., Sultanova, N., Taheri, S., Ozturk, G. (2021). Subgradient Smoothing Method for Nonsmooth Nonconvex Optimization. In: Al-Baali, M., Purnama, A., Grandinetti, L. (eds) Numerical Analysis and Optimization. NAO 2020. Springer Proceedings in Mathematics & Statistics, vol 354. Springer, Cham. https://doi.org/10.1007/978-3-030-72040-7_3

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