Template-Type: ReDIF-Paper 1.0
Author-Name: Brinkhuis, J.
Author-Name-Last: Brinkhuis
Author-Name-First: Jan
Author-Name: Zhang, S.
Author-Name-Last: Zhang
Author-Name-First: Shuzhong
Title: A D-induced duality and its applications
Abstract: This paper attempts to extend the notion of duality for convex cones, by basing it on a predescribed conic ordering and a fixed bilinear mapping. This is an extension of the standard definition of dual cones, in the sense that the nonnegativity of the inner-product is replaced by a pre-specified conic ordering, defined by a convex cone D, and the inner-product itself is replaced by a general multi-dimensional bilinear mapping. This new type of duality is termed the D-induced duality in the paper. We further introduce the notion of D-induced polar sets within the same framework, which can be viewed as a generalization of the D-induced polar sets within the same framework, which can be viewed as a generalization of the D-induced dual cones and are convenient to use for some practical applications. Properties of the extended duality, including the extended bi-polar theorem, are proven. Furthermore, attention is paid to the computation and approximation of the D-induced dual objects. We discuss, as examples, applications of the newly introduced D-induced duality concepts in robust conic optimization and the duality theory for multi-objective conic optimization.
Creation-Date: 2003-08-07
File-URL: https://repub.eur.nl/pub/1058/ei200342.pdf
File-Format: application/pdf
Series: RePEc:ems:eureir
Number: EI 2003-42
Keywords: bi-polar theorem, conic optimization, convex cones, duality
Handle: RePEc:ems:eureir:1058