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eng
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Description
In the research of mathematical programming, duality theorems are essential and important elements. Recently, Lagrange duality theorems for separable convex programming have been studied. Tseng proves that there is no duality gap in Lagrange duality for separable convex programming without any qualifications. In other words, although the infimum value of the primal problem equals to the supremum value of the Lagrange dual problem, Lagrange multiplier does not always exist. Jeyakumar and Li prove that Lagrange multiplier always exists without any qualifications for separable sublinear programming. Furthermore, Jeyakumar and Li introduce a necessary and sufficient constraint qualification for Lagrange duality theorem for separable convex programming. However, separable convex constraints do not always satisfy the constraint qualification, that is, Lagrange duality does not always hold for separable convex programming. In this paper, we study duality theorems for separable convex programming without any qualifications. We show that a separable convex inequality system always satisfies the closed cone constraint qualification for quasiconvex programming and investigate a Lagrange-type duality theorem for separable convex programming. In addition, we introduce a duality theorem and a necessary and sufficient optimality condition for a separable convex programming problem, whose constraints do not satisfy the Slater condition.
Subject
Separable convex programming
Duality theorem
Constraint qualification
Generator of quasiconvex functions
Journal Title
Journal of optimization theory and applications
Volume
172
Issue
2
Start Page
669
End Page
683
ISSN
00223239
Published Date
2017-02
DOI
DOI Date
2017-02-17
NCID
AA00253056
Publisher
Springer US
NII Type
Journal Article
Format
PDF
Rights
© Springer Science+Business Media New York 2016. The final publication is available at Springer via http://dx.doi.org/10.1007/s10957-016-1003-1.
Text Version
著者版
Gyoseki ID
e30815
e31982
OAI-PMH Set
Interdisciplinary Graduate School of Science and Engineering