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Center for Nonlinear Studies |
The development of primal-dual interior point methods for semidefinite programming in the late 1990's led to rapid growth in the use of semidefinite programming in many areas of application. A number of open source software packages for SDP were developed, and these solvers have proven to be quite capable of solving small to medium sized problems. However, the primal-dual interior point method is a second order method with storage requirements that grow quadratically with the number of constraints. There is now considerable interest in the development of first order methods for large scale SDP that can be used to solve these larger instances. In this talk I will review the primal-dual interior point method for SDP, discuss implementation issues including parallelization of the method, numerical accuracy, and storage requirements. I will also review some attempts to develop first order methods for large scale SDP and the unresolved issues surrounding these methods.
Host: Marian Anghel