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.

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