Gradient Sampling Methods

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 13 in Introduction to Nonsmooth Optimization, 2014, pp 311-312 from Springer

Abstract: Abstract One of the newest approaches in general nonsmooth optimization is to use gradient sampling algorithms developed by Burke, Lewis, and Overton. The gradient sampling method is a method for minimizing an objective function that is locally Lipschitz continuous and smooth on an open dense subset of $$\mathbb {R}^n$$ R n . The objective may be nonsmooth and/or nonconvex. Gradient sampling methods may be considered as a stabilized steepest descent algorithm. The central idea behind these techniques is to approximate the subdifferential of the objective function through random sampling of gradients near the current iteration point. In this chapter, we introduce the original gradient sampling algorithm.

Keywords: Objective Function; Line Search; Central Idea; Cluster Point; Open Dense Subset (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_13

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DOI: 10.1007/978-3-319-08114-4_13

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