How Far Can We Go With Primal-Dual Interior Point Methods for SDP?

Primal--dual interior point methods and the HKM method in particular have been implemented in a number of software packages for semidefinite programming. These methods have performed well in practice on small to medium sized SDP's. However, primal--dual codes have had some trouble in solving larger problems because of the method's storage requirements. In this paper we analyze the storage requirements of the HKM method and describe a 64-bit parallel implementation of the method that has been used to solve some large scale problems that have not previously been solved by primal--dual methods.


New Mexico Tech, February 28, 2005. A revised version of this paper has been accepted for publication in "Computational Optimization and Applications"