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Bundle Methods

In: Introduction to Nonsmooth Optimization

Author

Listed:
  • Adil Bagirov

    (School of Information Technology and Mathematical Sciences, University of Ballarat)

  • Napsu Karmitsa

    (University of Turku)

  • Marko M. Mäkelä

    (University of Turku)

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.

Suggested Citation

  • Adil Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2014. "Bundle Methods," Springer Books, in: Introduction to Nonsmooth Optimization, edition 127, chapter 0, pages 305-310, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-08114-4_12
    DOI: 10.1007/978-3-319-08114-4_12
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