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Discrete Gradient Methods

In: Numerical Nonsmooth Optimization

Author

Listed:
  • Adil M. Bagirov

    (Federation University Australia, School of Science, Engineering and Information Technology)

  • Sona Taheri

    (Federation University Australia, School of Science, Engineering and Information Technology)

  • Napsu Karmitsa

    (University of Turku, Department of Mathematics and Statistics)

Abstract

In this chapter, the notion of a discrete gradient is introduced and it is shown that the discrete gradients can be used to approximate subdifferentials of a broad class of nonsmooth functions. Two methods based on such approximations, more specifically, the discrete gradient method (DGM) and its limited memory version (LDGB), are described. These methods are semi derivative-free methods for solving nonsmooth and, in general, nonconvex optimization problems. The performance of the methods is demonstrated using some academic test problems.

Suggested Citation

  • Adil M. Bagirov & Sona Taheri & Napsu Karmitsa, 2020. "Discrete Gradient Methods," Springer Books, in: Adil M. Bagirov & Manlio Gaudioso & Napsu Karmitsa & Marko M. Mäkelä & Sona Taheri (ed.), Numerical Nonsmooth Optimization, chapter 0, pages 621-654, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-34910-3_18
    DOI: 10.1007/978-3-030-34910-3_18
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