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On Generalized Pseudo- and Quasiconvexity for Nonsmooth Functions

Marko M. Mäkelä, Napsu Karmitsa, Ville-Pekka Eronen, On Generalized Pseudo- and Quasiconvexity for Nonsmooth Functions. TUCS Technical Reports 989, Turku Centre for Computer Science, 2010.

Abstract:

Convexity plays a crucial role in mathematical optimization theory. In order to extend the existing results depending on convexity, numerous attempts of generalizing the concept have been published during years. Different types of generalized convexities has proved to be the main tool when constructing optimality conditions, particularly sufficient conditions for optimality.

The purpose of this paper is to 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.

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BibTeX entry:

@TECHREPORT{tMaKaEr10a,
  title = {On Generalized Pseudo- and Quasiconvexity for Nonsmooth Functions},
  author = {Mäkelä, Marko M. and Karmitsa, Napsu and Eronen, Ville-Pekka},
  number = {989},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2010},
  keywords = {Generalized convexity, Clarke's derivatives, Nonsmooth analysisi},
  ISBN = {978-952-12-2496-6},
}

Belongs to TUCS Research Unit(s): Other

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