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language
eng
Author
Suzuki, Satoshi Department of Mathematics, Interdisciplinary Graduate School of Science and Engineering, Shimane University
Kuroiwa, Daishi Department of Mathematics, Interdisciplinary Graduate School of Science and Engineering, Shimane University
Description
Characterizations of the solution set in terms of subdifferentials play an important role in research of mathematical programming. Previous characterizations are based on necessary and sufficient optimality conditions and invariance properties of subdifferentials. Recently, characterizations of the solution set for essentially quasiconvex programming in terms of Greenberg–Pierskalla subdifferential are studied by the authors. Unfortunately, there are some examples such that these characterizations do not hold for non-essentially quasiconvex programming. As far as we know, characterizations of the solution set for non-essentially quasiconvex programming have not been studied yet. In this paper, we study characterizations of the solution set in terms of subdifferentials for non-essentially quasiconvex programming. For this purpose, we use Martínez–Legaz subdifferential which is introduced by Martínez–Legaz as a special case of c-subdifferential by Moreau. We derive necessary and sufficient optimality conditions for quasiconvex programming by means of Martínez–Legaz subdifferential, and, as a consequence, investigate characterizations of the solution set in terms of Martínez–Legaz subdifferential. In addition, we compare our results with previous ones. We show an invariance property of Greenberg–Pierskalla subdifferential as a consequence of an invariance property of Martínez–Legaz subdifferential. We give characterizations of the solution set for essentially quasiconvex programming in terms of Martínez–Legaz subdifferential.
Subject
Quasiconvex programming
Solution set
Subdifferential
Optimality condition
Journal Title
Optimization letters
Volume
11
Issue
8
Start Page
1699
End Page
1712
ISSN
18624472
Published Date
2017-12
DOI
DOI Date
2017-12-01
NCID
AA12249544
Publisher
Springer-Verlag
NII Type
Journal Article
Format
PDF
Rights
© Springer-Verlag Berlin Heidelberg 2016
The full-text file will be made open to the public on January 1, 2018 in accordance with publisher's 'Terms and Conditions for Self-Archiving'.
Text Version
著者版
Gyoseki ID
e32907
OAI-PMH Set
Interdisciplinary Graduate School of Science and Engineering
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