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Discrete Gradient Method: Derivative-Free Method for Nonsmooth Optimization

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Abstract

A new derivative-free method is developed for solving unconstrained nonsmooth optimization problems. This method is based on the notion of a discrete gradient. It is demonstrated that the discrete gradients can be used to approximate subgradients of a broad class of nonsmooth functions. It is also shown that the discrete gradients can be applied to find descent directions of nonsmooth functions. The preliminary results of numerical experiments with unconstrained nonsmooth optimization problems as well as the comparison of the proposed method with the nonsmooth optimization solver DNLP from CONOPT-GAMS and the derivative-free optimization solver CONDOR are presented.

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Authors and Affiliations

  1. Centre for Informatics and Applied Optimization, School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria, 3353, Australia

    A. M. Bagirov

  2. Department of Mathematics & Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey

    B. Karasözen

  3. Department of Mathematics, Middle East Technical University, Ankara, Turkey

    M. Sezer

Authors
  1. A. M. Bagirov
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  2. B. Karasözen
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  3. M. Sezer
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Correspondence to A. M. Bagirov.

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Communicated by F. Giannessi.

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Bagirov, A.M., Karasözen, B. & Sezer, M. Discrete Gradient Method: Derivative-Free Method for Nonsmooth Optimization. J Optim Theory Appl 137, 317–334 (2008). https://doi.org/10.1007/s10957-007-9335-5

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