##
Complete Classification of Self-scaled Barrier Functions

###
Stefan H. Schmieta

Self-scaled barrier functions are an important tool in
the study of conic linear programming problems over
symmetric cones. They are also closely related to
Euclidean Jordan algebras. In the first part of this
article we show that every self-scaled barrier function
defines a Euclidean Jordan algebra. In the second part
we use this algebra to obtain a complete classification
of self-scaled barrier functions. In particular we show
that the barrier function with the smallest possible
self-concordance parameter is unique up to an additive
constant and can be written in terms of the determinant
of the associated Jordan algebra.
TR-2000-01 (July 2000),
CORC, Columbia University, New York, NY

Contact: schmieta@firulete.ieor.columbia.edu