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CHARACTERIZATIONS OF QUASICONVEX AND PSEUDOCONVEX FUNCTIONS BY THEIR SECOND-ORDER REGULAR SUBDIFFERENTIALS

Part of: Functions of several variables Existence theories

Published online by Cambridge University Press:  30 April 2019

MOHAMMAD TAGHI NADI  and
JAFAR ZAFARANI Open the ORCID record for JAFAR ZAFARANI [Opens in a new window]
MOHAMMAD TAGHI NADI
Affiliation:
University of Isfahan, Isfahan, 81745-163, Iran email mt_nadi@yahoo.com
JAFAR ZAFARANI*
Affiliation:
University of Isfahan and Sheikhbahaee University, Isfahan, 81745-163, Iran email jzaf@zafarani.ir
*
✉jzaf@zafarani.ir
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Abstract

We present the second-order necessary and sufficient conditions for quasiconvex and pseudoconvex functions in terms of their second-order regular subdifferentials.

Keywords

quasiconvexitysecond-order subdifferentialpositive semidefinite propertysecond-order optimality conditions

MSC classification

Primary: 26B25: Convexity, generalizations
Secondary: 49J40: Variational methods including variational inequalities 49J52: Nonsmooth analysis 49J53: Set-valued and variational analysis
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 109 , Issue 2 , October 2020 , pp. 217 - 229
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Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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