Generalized Convexities

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 5 in Introduction to Nonsmooth Optimization, 2014, pp 139-168 from Springer

Abstract: Abstract Convexity plays a crucial role in mathematical optimization theory. Especially, in duality theory and in constructing optimality conditions, convexity has been the most important concept since the basic reference by Rockafellar was published. Different types of generalized convexities have proved to be the main tool when constructing optimality conditions, particularly sufficient conditions for optimality. In this chapter, we analyze the properties of the generalized pseudo- and quasiconvexities for nondifferentiable locally Lipschitz continuous functions. The treatment is based on the Clarke subdifferentials and generalized directional derivatives.

Keywords: Quasiconvex; Mathematical Optimization Theory; Clarke Subdifferential; Subdifferential Regularity; Pseudomonotonicity (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_5

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DOI: 10.1007/978-3-319-08114-4_5

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