A D-induced duality and its applications

Jan Brinkhuis and Shuzhong Zhang

No EI 2002-34, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

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. Basic properties of the extended duality, including the extended bi-polar theorem, are proven. Examples are give to show the applications of the new results.

Keywords: Bi-polar theorem; Conic optimization; Convex cones; Duality (search for similar items in EconPapers)
Date: 2002-10-02
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