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eng
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Description
In mathematical programming, duality theorems play a central role. Especially, in convex and quasiconvex programming, Lagrange duality and surrogate duality have been studied extensively. Additionally, constraint qualifications are essential ingredients of the powerful duality theory. The best-known constraint qualifications are the interior point conditions, also known as the Slater-type constraint qualifications. A typical example of mathematical programming is a minimization problem of a real-valued function on a vector space. This types of problems have been studied widely and have been generalized in several directions. Recently, the authors investigate set functions and Fenchel duality. However, duality theorems and its constraint qualifications for mathematical programming with set functions have not been studied yet. It is expected to study set functions and duality theorems. In this paper, we study duality theorems for convex and quasiconvex set functions. We show Lagrange duality theorem for convex set functions and surrogate duality theorem for quasiconvex set functions under the Slater condition. As an application, we investigate an uncertain problem with motion uncertainty.
Journal Title
SN Operations Research Forum
Volume
1
ISSN
2662-2556
Published Date
2020.2.21
DOI
Publisher
Springer International Publishing
NII Type
Journal Article
Format
PDF
Text Version
著者版
OAI-PMH Set
Faculty of Science and Engineering
Remark
This is a post-peer-review, pre-copyedit version of an article published in SN Operations Research Forum. The final authenticated version is available online at: http://dx.doi.org/10.1007/s43069-020-0005-x