A D-induced duality and its applications
2002-10-02
Research Paper
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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
Automatically Extracted Terms
- duality
- mapping
- space
- d-induced
- d-induced duality
- product
- theorem
- solution
- proposition
- optimization
- condition
- result
- xt ak y
- vector
- surjective
- problem
- application
- tensor product
- order
- non-flat
