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A D-induced duality and its applications

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  • Brinkhuis, J.
  • Zhang, S.

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.

Suggested Citation

  • Brinkhuis, J. & Zhang, S., 2002. "A D-induced duality and its applications," Econometric Institute Research Papers EI 2002-34, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:547
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    References listed on IDEAS

    as
    1. Sturm, J.F. & Zhang, S., 2001. "On Cones of Nonnegative Quadratic Functions," Other publications TiSEM 075a6b4d-5b51-4153-a9c3-0, Tilburg University, School of Economics and Management.
    2. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
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