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Zbl 1008.90046
Hauser, Raphael A.; Lim, Yongdo
Self-scaled barriers for irreducible symmetric cones. (English)
[J] SIAM J. Optim. 12, No.3, 715-723 (2002). ISSN 1052-6234; ISSN 1095-7189/e

Summary: Self-scaled barrier functions are fundamental objects in the theory of interior-point methods for linear optimization over symmetric cones, of which linear and semidefinite programming are special cases. In this article we classify the special class of self-scaled barriers which are defined on irreducible symmetric cones. Together with a decomposition theorem for general self-scaled barriers this concludes the algebraic classification theory of these functions.

MSC 2000:: *90C25 Convex programming
52A41 Convex functions and convex programs (convex geometry)
90C60 Abstract computational complexity for math. programming problems
90C05 Linear programming
90C20 Quadratic programming

Keywords: semidefinite programming; self-scaled barrier functions; interior-point methods; symmetric cones; Euclidean Jordan algebras

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Zentralblatt MATH Berlin [Germany]