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Title Alternative (English)
Karush–Kuhn–Tucker type optimality condition for quasiconvex programming in terms of Greenberg–Pierskalla subdifferential
Author
Description
In the research of optimization problems, optimality conditions play an important role. By using some derivatives, various types of necessary and/or sufficient optimality conditions have been introduced by many researchers. Especially, in convex programming, necessary and sufficient optimality conditions in terms of the subdifferential have been studied extensively. Recently, necessary and sufficient optimality conditions for quasiconvex programming have been investigated by the authors. However, there are not so many results concerned with Karush–Kuhn–Tucker type optimality conditions for non-differentiable quasiconvex programming. In this paper, we study a Karush–Kuhn–Tucker type optimality condition for quasiconvex programming in terms of Greenberg–Pierskalla subdifferential. We show some closedness properties for Greenberg–Pierskalla subdifferential. Under the Slater constraint qualification, we show a necessary and sufficient optimality condition for essentially quasiconvex programming in terms of Greenberg–Pierskalla subdifferential. Additionally, we introduce a necessary and sufficient constraint qualification of the optimality condition. As a corollary, we show a necessary and sufficient optimality condition for convex programming in terms of the subdifferential.
Subject
Optimality condition
Quasiconvex programming
Subdifferential
Constraint qualification
Journal Title
Journal of Global Optimization
Volume
79
Start Page
191
End Page
202
Published Date
2021-01
DOI
Publisher
Springer Nature
NII Type
Journal Article
Format
PDF
Rights
This is a post-peer-review, pre-copyedit version of an article published in Journal of Global Optimization. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10898-020-00926-8
Text Version
著者版
OAI-PMH Set
Faculty of Science and Engineering