Duality Theorems for Convex and Quasiconvex Set Functions

SN Operations Research Forum Volume 1 published_at 2020-2-21
アクセス数 : 1196
ダウンロード数 : 91

今月のアクセス数 : 51
今月のダウンロード数 : 2
File
Title
Duality Theorems for Convex and Quasiconvex Set Functions
Creator
Source Title
SN Operations Research Forum
Volume 1
Journal Identifire
ISSN 2662-2556
Descriptions
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.
Subjects
Set function ( Other)
Lagrange duality ( Other)
Surrogate duality ( Other)
Mathematical programming with uncertainty ( Other)
Language
eng
Resource Type journal article
Publisher
Springer International Publishing
Date of Issued 2020-2-21
Publish Type Accepted Manuscript
Access Rights open access
Relation
[DOI] 10.1007/s43069-020-0005-x
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