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Current Research in Nonlinear Analysis pp 129–155Cite as

On Generalized Pseudo- and Quasiconvexities for Nonsmooth Functions

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 135))

Abstract

Convexity is the most important and useful concept 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 have proved to be the main tool when constructing optimality conditions, in particular sufficient conditions for optimality. The aim 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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Acknowledgements

We want to thank the Academy of Finland (Project No. 289500 and 294002).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Turku, Turku, Finland

    Ville-Pekka Eronen, Marko M. Mäkelä & Napsu Karmitsa

Authors
  1. Ville-Pekka Eronen
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  2. Marko M. Mäkelä
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  3. Napsu Karmitsa
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Corresponding author

Correspondence to Ville-Pekka Eronen .

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Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Eronen, VP., Mäkelä, M.M., Karmitsa, N. (2018). On Generalized Pseudo- and Quasiconvexities for Nonsmooth Functions. In: Rassias, T. (eds) Current Research in Nonlinear Analysis. Springer Optimization and Its Applications, vol 135. Springer, Cham. https://doi.org/10.1007/978-3-319-89800-1_6

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