Dr. Stefan Schmieta
Axioma Inc, and Columbia University
This talk will review recent results in interior-point algorithms for
convex optimization. In their seminal work, Nesterov and Nemirovski
showed that a convex optimization problem can be solved in a
polynomial number of iterations if a suitable barrier for its feasible
region exists. They called such a barrier self-concordant. We will
discuss their basic results and then move on to the special case of
self-scaled barriers that was introduced by Nesterov and Todd. This
class of optimization problems, which includes linear, semi-definite,
and second-order cone programming, has been subject of intense
research in the last years.