Approximations of Subdifferentials

Adil Bagirov (), Napsu Karmitsa () and Marko M. Mäkelä ()
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Adil Bagirov: School of Information Technology and Mathematical Sciences, University of Ballarat
Napsu Karmitsa: University of Turku
Marko M. Mäkelä: University of Turku

Chapter Chapter 6 in Introduction to Nonsmooth Optimization, 2014, pp 169-197 from Springer

Abstract: Abstract In practice, the computation of subdifferential is not an easy task. In this chapter, we first consider some families of set-valued mappings that can be used to approximate subdifferentials. Then we define the concept of a discrete gradient that can be used as an approximation of the subgradient at a given point. Finally, we introduce the notion of piecewise partially separable functions and study their properties. In particular, we describe how to calculate the discrete gradient for a piecewise partially separable function.

Keywords: Subdifferential; Discrete Gradient; Partial Separation; Subgradient; Directional Differentiability (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-08114-4_6

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DOI: 10.1007/978-3-319-08114-4_6

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