- A D-Induced Duality and Its Applications Jan Brinkhuis (brinkhuisfew.eur.nl) Shuzhong Zhang (zhangse.cuhk.edu.hk) Abstract: This paper attempts to extend the notion of duality for convex cones, by basing it on a pre-described conic ordering and a fixed bilinear mapping. This is an extension of the standard definition of dual cones, in the sense that the {\em 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 {\em $D$-induced duality}\/ in the paper. Basic properties of the extended duality, including the extended bi-polar theorem, are proven. Examples are given to show the applications of the new results. Keywords: convex cones, duality, bi-polar theorem, conic optimization Category 1: Linear, Cone and Semidefinite Programming Category 2: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: Technical Report SEEM2002-01,Department of Systems Engineering & Engineering Management, The Chinese University of Hong Kong, 2002. Download: [Postscript]Entry Submitted: 09/20/2002Entry Accepted: 09/21/2002Entry Last Modified: 09/20/2002Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.