Characterization of the barrier parameter of homogeneous convex cones

Characterization of the barrier parameter of homogeneous convex cones

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Article ID: iaor19992584
Country: Netherlands
Volume: 81
Issue: 1
Start Page Number: 55
End Page Number: 76
Publication Date: Mar 1998
Journal: Mathematical Programming
Authors: ,
Abstract:

We characterize the smallest (best) barrier parameter of self-concordant barriers for homogeneous convex cones. In particular, we prove that this parameter is the same as the rank of the cone which is the number of steps in a recursive construction of the cone (Siegel domain construction). We also provide lower bounds on the barrier parameter in terms of the Carathéodory number of the cone. The bounds are tight for homogeneous self-dual cones.

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