Optimality Conditions

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 4 in Introduction to Nonsmooth Optimization, 2014, pp 117-137 from Springer

Abstract: 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.

Keywords: Unconstrained Nonsmooth Optimization; Subgradient Information; Descent Direction; Geometrical Optimality Condition; Nonsmooth Analysis (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_4

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DOI: 10.1007/978-3-319-08114-4_4

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