ON THE NESTEROV-TODD DIRECTION IN SEMIDEFINITE PROGRAMMING

We study different choices of search direction for primal-dual interio r-point methods for semidefinite programming problems. One particular choice we consider comes from a specialization of a class of algorithm s developed by Nesterov and Todd for certain convex programming proble ms. We discuss how the search directions for the Nesterov{Todd (NT) me thod can be computed efficiently and demonstrate how they can be viewe d as Newton directions. This last observation also leads to convenient computation of accelerated steps, using the Mehrotra predictor-correc tor approach, in the NT framework. We also provide an analytical and n umerical comparison of several methods using different search directio ns, and suggest that the method using the NT direction is more robust than alternative methods.