*********************************
There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
*********************************
We describe a general idea of path-following algorithms for solving
optimization problems. The concept of the universal barrier function (u.b.f) is introduced.
The key result of Yu. Nesterov and A.Nemirovsky allowing to obtain excellent complexity estimates is explained. Finally, we describe new results related to computations of u.b. fs for a very broad class of cones generated by Chebyshev systems. Connections with classical work of M. Krein , A. Nudelman and I. Schoenberg are explained. New results allow one to substantially extend the
domain of applicability of modern interior-point algorithms.
