Discrete Gradient Methods

Adil M. Bagirov (), Sona Taheri () and Napsu Karmitsa ()
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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

Chapter Chapter 18 in Numerical Nonsmooth Optimization, 2020, pp 621-654 from Springer

Abstract: 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.

Date: 2020
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DOI: 10.1007/978-3-030-34910-3_18

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