CHARACTERIZATION OF THE BARRIER PARAMETER OF HOMOGENEOUS CONVEX CONES

Authors
GULER O TUNCEL L
Citation
O. Guler et L. Tuncel, CHARACTERIZATION OF THE BARRIER PARAMETER OF HOMOGENEOUS CONVEX CONES, Mathematical programming, 81(1), 1998, pp. 55-76
Citations number
18
Categorie Soggetti
Operatione Research & Management Science",Mathematics,"Computer Science Software Graphycs Programming","Operatione Research & Management Science",Mathematics,"Computer Science Software Graphycs Programming
Journal title
Mathematical programming → ACNP
ISSN journal
00255610
Volume
81
Issue
1
Year of publication
1998
Pages
55 - 76
Database
ISI
SICI code
0025-5610(1998)81:1<55:COTBPO>2.0.ZU;2-0
Abstract
We characterize the smallest (best) barrier parameter of self-concorda nt barriers for homogeneous convex cones. In particular, we prove that this parameter is the same as the rank of the cone which is the numbe r of steps in a recursive construction of the cone (Siegel domain cons truction). We also provide lower bounds on the barrier parameter in te rms of the Caratheodory number of the cone. The bounds are tight for h omogeneous self-dual cones. (C) 1998 The Mathematical Programming Soci ety. Inc, Published by Elsevier Science B.V.