Self-Scaled Barrier Functions on Symmetric Cones and Their Classification

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dc.citation.epage143en_US
dc.citation.issueNumber2en_US
dc.citation.spage121en_US
dc.citation.volumeNumber2en_US
dc.contributor.authorHauser, R.A.en_US
dc.contributor.authorGüler O.en_US
dc.date.accessioned2016-02-08T10:31:20Z
dc.date.available2016-02-08T10:31:20Z
dc.date.issued2002en_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractSelf-scaled barrier functions on self-scaled cones were axiomatically introduced by Nesterov and Todd in 1994 as a tool for the construction of primal-dual long-step interior point algorithms. This paper provides firm foundations for these objects by exhibiting their symmetry properties, their close ties with the symmetry groups of their domains of definition, and subsequently their decomposition into irreducible parts and their algebraic classification theory. In the first part we recall the characterization of the family of self-scaled cones as the set of symmetric cones and develop a primal-dual symmetric viewpoint on self-scaled barriers, results that were first discovered by the second author. We then show in a short, simple proof that any pointed, convex cone decomposes into a direct sum of irreducible components in a unique way, a result which can also be of independent interest. We then proceed to showing that any self-scaled barrier function decomposes, in an essentially unique way, into a direct sum of self-scaled barriers defined on the irreducible components of the underlying symmetric cone. Finally, we present a complete algebraic classification of self-scaled barrier functions using the correspondence between symmetric cones and Euclidean-Jordan algebras.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T10:31:20Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2002en
dc.identifier.issn16153375
dc.identifier.urihttp://hdl.handle.net/11693/24576
dc.language.isoEnglishen_US
dc.source.titleFoundations of Computational Mathematicsen_US
dc.subjectDecomposition of convex conesen_US
dc.subjectInterior-point methodsen_US
dc.subjectJordan algebrasen_US
dc.subjectSelf-scaled barrier functionsen_US
dc.subjectSymmetric conesen_US
dc.subjectUniversal barrier functionen_US
dc.subjectBarrier functionsen_US
dc.subjectConvex coneen_US
dc.subjectInterior-point methoden_US
dc.subjectJordan algebraen_US
dc.subjectSymmetric coneen_US
dc.subjectBarrier functionsen_US
dc.subjectConvex coneen_US
dc.subjectInterior-point methoden_US
dc.subjectJordan algebraen_US
dc.subjectSymmetric coneen_US
dc.subjectConesen_US
dc.subjectAlgebraen_US
dc.subjectConesen_US
dc.subjectAlgebraen_US
dc.subjectConvex optimizationen_US
dc.titleSelf-Scaled Barrier Functions on Symmetric Cones and Their Classificationen_US
dc.typeArticleen_US

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