On the optimal parameter of a self-concordant barrier over a symmetric cone

• Type: Article in International Scientific Journal
• Date: 2006

Authors

Domingos Moreira Cardoso (Author) Other; Luís Almeida Vieira (Author) FEUP

Journal

Title: European Journal of Operational Research

Vol. 169

Pages: 1148-1157

ISSN: 0377-2217

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 8 Citations

ISI Web of Science

Scopus - 17 Citations

Scientific classification

FOS: Engineering and technology > Other engineering and technologies

CORDIS: Physical sciences > Mathematics > Algebra ; Physical sciences > Mathematics > Applied mathematics > Operations research

Other information

Authenticus ID: P-004-MQM

DOI: 10.1016/j.ejor.2004.11.027

Abstract (EN): The properties of the barrier F(x) = -log(det(x)), defined over the cone of squares of a Euclidean Jordan algebra, are analyzed using pure algebraic techniques. Furthermore, relating the Caratheodory number of a symmetric cone with the rank of an underlying Euclidean Jordan algebra, conclusions about the optimal parameter of F are suitably obtained. Namely, in a more direct and suitable way than the one presented by Guler and Tuncel (Characterization of the barrier parameter of homogeneous convex cones, Mathematical Programming 81 (1998) 55-76), it is proved that the Caratheodory number of the cone of squares of a Euclidean Jordan algebra is equal to the rank of the algebra. Then, taking into account the result obtained in the same paper where it is stated that the Caratheodory number of a symmetric cone Q is the optimal parameter of a self-concordant barrier defined over Q, we may conclude that the rank of every underlying Euclidean Jordan algebra is also the self-concordant barrier optimal parameter.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 10