language
eng
Author
Description
In mathematical programming, various kinds of optimality conditions have been introduced. In the research of optimality conditions, some types of subdifferentials play an important role. Recently, by using Greenberg–Pierskalla subdifferential and Martínez-Legaz subdifferential, necessary and sufficient optimality conditions for quasiconvex programming have been introduced. On the other hand, constraint qualifications are essential elements for duality theory in mathematical programming. Over the last decade, necessary and sufficient constraint qualifications for duality theorems have been investigated extensively. Recently, by using the notion of generator, necessary and sufficient constraint qualifications for Lagrange-type duality theorems have been investigated. However, constraint qualifications for optimality conditions in terms of Greenberg–Pierskalla subdifferential and Martínez-Legaz subdifferential have not been investigated yet. In this paper, we study optimality conditions and constraint qualifications for quasiconvex programming. We introduce necessary and sufficient optimality conditions in terms of Greenberg–Pierskalla subdifferential, Martínez-Legaz subdifferential and generators. We investigate necessary and/or sufficient constraint qualifications for these optimality conditions. Additionally, we show some equivalence relations between duality results for convex and quasiconvex programming.
Subject
Quasiconvex programming
Optimality condition
Constraint qualification
Generator of a quasiconvex function
Journal Title
Journal of Optimization Theory and Applications
Volume
183
Issue
3
Start Page
963
End Page
976
ISSN
0022-3239
ISSN(Online)
1573-2878
Published Date
2019-12
DOI
Publisher
Springer
NII Type
Journal Article
Format
PDF
Text Version
著者版
Gyoseki ID
e36991
OAI-PMH Set
Faculty of Science and Engineering
Remark
;学外公開