Largest dual ellipsoids inscribed in dual cones

M. J. Todd (miketoddcs.cornell.edu)

Abstract: Suppose x and s lie in the interiors of a cone K and its dual K^* respectively. We seek dual ellipsoidal norms such that the product of the radii of the largest inscribed balls centered at x and s and incribed in K and K^* respectively is maximized. Here the balls are defined using the two dual norms. We provide a solution when the cones are symmetric, that is self-dual and homogeneous. This provides a geometric justification for the Nesterov-Todd primal-dual scaling in symmetric cone programming.

Keywords: Dual cones, inscribed ellipsoids, conic programming

Category 1: Linear, Cone and Semidefinite Programming

Citation: Technical Report No. 1426, School of Operations Research and Industrial Engineering, Cornell University

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Entry Submitted: 06/23/2005
Entry Accepted: 06/23/2005
Entry Last Modified: 06/23/2005

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