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Optimization in Science and Engineering pp 1–32Cite as

Piecewise Linear Classifiers Based on Nonsmooth Optimization Approaches

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Abstract

Nonsmooth optimization provides efficient algorithms for solving many machine learning problems. In particular, nonsmooth optimization approaches to supervised data classification problems lead to the design of very efficient algorithms for their solution. In this chapter, we demonstrate how nonsmooth optimization algorithms can be applied to design efficient piecewise linear classifiers for supervised data classification problems. Such classifiers are developed using a max–min and a polyhedral conic separabilities as well as an incremental approach. We report results of numerical experiments and compare the piecewise linear classifiers with a number of other mainstream classifiers.

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Acknowledgements

R. Kasimbeyli and G. Özturk are the recipients of a grant of the Scientific and Technological Research Council of Turkey—TUBITAK (Project number:107M472).

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Authors and Affiliations

  1. School of Science, Information Technology and Engineering, Federation University, Australia, Ballarat, VIC, 3353, Australia

    Adil M. Bagirov & Julien Ugon

  2. Department of Industrial Engineering, Anadolu University, Eskisehir, 26480, Turkey

    Refail Kasimbeyli & Gürkan Öztürk

Authors
  1. Adil M. Bagirov
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  2. Refail Kasimbeyli
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  3. Gürkan Öztürk
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  4. Julien Ugon
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Corresponding author

Correspondence to Adil M. Bagirov .

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Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Princeton University Dept. Chemical Engineering, Princeton, New Jersey, USA

    Christodoulos A. Floudas

  3. Dept. Industrial & Systems Engineering, Texas A&M University, College Station, Texas, USA

    Sergiy Butenko

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Bagirov, A.M., Kasimbeyli, R., Öztürk, G., Ugon, J. (2014). Piecewise Linear Classifiers Based on Nonsmooth Optimization Approaches. In: Rassias, T., Floudas, C., Butenko, S. (eds) Optimization in Science and Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0808-0_1

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