ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

17. Control Theory and Optimization

1991 MS Classification: 17, 90, 49 Faybusovich, Leonid, University of Notre Dame, USA Interior-point algorithms and Euclidean Jordan algebras Each symmetric cone can be realized as a cone of squares in an Euclidean Jordan algebra. This enables us to develop a fairly complete theory of interior-point algorithms for optimization problems defined on the intersection of a symmetric cone and an affine subspace. The optimal (in the sense of the theory of interior-point algorithms ) choice of the barrier function is log det, where det function is defined on an arbitrary Jordan algebra. The complexity estimates for major classes of interior-point algorithms are given in terms of the rank and the degree of the Euclidean Jordan algebra corresponding to a given symmetric cone. Reference: L. Faybusovich, Euclidean Jordan algebras and Interior-point algorithms (to appear in Positivity)