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Cutting Plane 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

Subgradient methods described in the previous chapter use only one arbitrary subgradient (generalized gradient) at a time, without memory of past iterations. If the information from previous iterations is kept, it is possible to define a model—the so-called cutting plane model—of the objective function. 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 basic ideas of the standard cutting plane method and then the more advanced cutting plane method with proximity control.

Suggested Citation

  • Adil Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2014. "Cutting Plane Methods," Springer Books, in: Introduction to Nonsmooth Optimization, edition 127, chapter 0, pages 299-303, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-08114-4_11
    DOI: 10.1007/978-3-319-08114-4_11
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