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.

Bi-polar theorem, Conic optimization, Convex cones, Duality
hdl.handle.net/1765/547
Econometric Institute Research Papers
Erasmus School of Economics

Brinkhuis, J, & Zhang, S. (2002). A D-induced duality and its applications (No. EI 2002-34). Econometric Institute Research Papers. Retrieved from http://hdl.handle.net/1765/547