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Largest dual ellipsoids inscribed in dual cones.
- Source :
-
Mathematical Programming . Mar2009, Vol. 117 Issue 1/2, p425-434. 10p. - Publication Year :
- 2009
-
Abstract
- Suppose x̄ and s̄ 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 x̄ and s̄ and inscribed in K and K *, respectively, is maximized. Here the balls are defined using the two dual norms. When the cones are symmetric, that is self-dual and homogeneous, the solution arises directly from the Nesterov–Todd primal–dual scaling. This shows a desirable geometric property of this scaling in symmetric cone programming, namely that it induces primal/dual norms that maximize the product of the distances to the boundaries of the cones. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00255610
- Volume :
- 117
- Issue :
- 1/2
- Database :
- Academic Search Index
- Journal :
- Mathematical Programming
- Publication Type :
- Academic Journal
- Accession number :
- 32960988
- Full Text :
- https://doi.org/10.1007/s10107-007-0171-z