Self-concordant barriers for cones generated by Chebyshev systems

Leonid Faybusovich

We explicitly calculate characteristic functions of cones of generalized polynomials corresponding to Chebyshev systems on intervals of the real line and the circle. Thus, in principal, we calculate homogeneous self-concordant barriers for this class of cones. This class includes almost all "cones of squares" considered by Nesterov. Oyr construction, however, does not use this structure and is applicable to a much broader class of cones. Even for "cones of squares" within the considered class our results are new.

Technical Report, January 2001. Available from the author's web site.