ファイル
言語
英語
著者
内容記述(抄録等)
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.
主題
Separable convex programming
Duality theorem
Constraint qualification
Generator of quasiconvex functions
掲載誌名
Journal of optimization theory and applications
172
2
開始ページ
669
終了ページ
683
ISSN
00223239
発行日
2017-02
DOI
DOI公開日
2017-02-17
NCID
AA00253056
出版者
Springer US
資料タイプ
学術雑誌論文
ファイル形式
PDF
権利関係
© 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.
著者版/出版社版
著者版
業績ID
e30815
e31982
部局
(旧組織)大学院総合理工学研究科 数理科学領域