Bundle Methods

Adil Bagirov (), Napsu Karmitsa () and Marko M. Mäkelä ()
Additional contact information
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 12 in Introduction to Nonsmooth Optimization, 2014, pp 305-310 from Springer

Abstract: Abstract At the moment, bundle methods are regarded as the most effective and reliable methods for nonsmooth optimization. They are based on the subdifferential theory developed by Rockafellar and Clarke, where the classical differential theory is generalized for convex and locally Lipschitz continuous functions, respectively. The basic idea of bundle methods is to approximate the subdifferential (that is, the set of subgradients) of the objective function by gathering subgradients from previous iterations into a bundle. In this way, more information about the local behavior of the function is obtained than what an individual arbitrary subgradient can yield. In this chapter, we first introduce the most frequently used bundle methods, that is, the proximal bundle and the bundle trust methods, and then we describe the basic ideas of the second order bundle-Newton method.

Keywords: Bundle Trust Method (BT); Proximal Bundle; Arbitrary Subgradient; Stored Subgradients; Classical Trust Region Methods (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-08114-4_12

Ordering information: This item can be ordered from
http://www.springer.com/9783319081144

DOI: 10.1007/978-3-319-08114-4_12

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().