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Disciplined convex programming
- Global Optimization: From Theory to Implementation, Nonconvex Optimization and Its Application Series
, 2006
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A D-Induced Duality and Its Applications
, 2002
"... 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 con ..."
Abstract
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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 given to show the applications of the new results. Keywords: Convex cones, duality, bi-polar theorem, conic optimization.
