Self-concordant barriers for cones generated by Chebyshev systems
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.