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Optimality Conditions

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

We present some results connecting the theories of nonsmooth analysis and optimization. We first define global and local minima of functions. After that, we generalize the classical first order optimality conditions for unconstrained nonsmooth optimization. Furthermore, we define linearizations for locally Lipschitz continuous functions by using subgradient information, and present their basic properties. These linearizations are suitable for function approximation. Finally, we define the notion of a descent direction and show how to find it for a locally Lipschitz continuous function.

Suggested Citation

  • Adil Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2014. "Optimality Conditions," Springer Books, in: Introduction to Nonsmooth Optimization, edition 127, chapter 0, pages 117-137, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-08114-4_4
    DOI: 10.1007/978-3-319-08114-4_4
    as

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