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Characterization of Nonsmooth Quasiconvex Functions and their Greenberg–Pierskalla’s Subdifferentials Using Semi-Quasidifferentiability notion

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Abstract

The relationships between Greenberg–Pierskalla’s subdifferential and some variants of it and semi-quasidifferentials of quasiconvex functions are studied in this paper. Also, some characterizations of quasiconvex functions in terms of semi-quasidifferentials and the connection between quasimonotonicity of semi-quasidifferentials and quasiconvexity are investigated.

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Acknowledgements

The author would like to express his gratitude to the associate editor and anonymous referees for their helpful comments on the first version of this paper. The author also thanks Professor M. Soleimani-damaneh for useful discussions. This research was in part supported by a grant from IPM (No. 99900034).

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Authors and Affiliations

  1. Mathematics Group, Department of Environment, Urmia University of Technology, Urmia, Iran

    Alireza Kabgani

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    Alireza Kabgani

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  1. Alireza Kabgani
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Correspondence to Alireza Kabgani.

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Communicated by Nicolas Hadjisavvas.

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Kabgani, A. Characterization of Nonsmooth Quasiconvex Functions and their Greenberg–Pierskalla’s Subdifferentials Using Semi-Quasidifferentiability notion. J Optim Theory Appl 189, 666–678 (2021). https://doi.org/10.1007/s10957-021-01851-w

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