On primal-dual path following algorithms for semidefinite programming.
E. de Klerk, C. Roos, T. Terlaky
Interior point methods for semidefinite programming have recently been
studied intensively, due to their polynomial complexity and practical
efficiency. Most of these methods are extensions of linear programming
algorithms. The long step primal-dual path-following (log barrier) method was rece
extended to semidefinite programming by Jiang, using the Nesterov-Todd
direction and a new centrality measure. In this report we refine and
extend this analysis: A weaker condition for a full Newton step
in terms of the new measure is derived, and quadratic convergence
to target points on the central path is shown. Moreover, strategies
for large barrier parameter updates which still allow full Newton
steps are proposed.
Report 96-102, Reports of the Faculty of Technical Mathematics and
Informatics, Delft University of Technology, Delft, The Netherlands.