Efficient parallel software for large-scale Semidefinite Programs

SemiDefinite Program (SDP) is one of principal problems in mathematical programming. Its application range is very wide and covers some problems arising from control theory; for example, a stability condition for differential inclusions and discrete-time optimal control problems. Solving these applications, however, sometimes requires long computation time, since they generate largescale SDPs. When Primal-Dual Interior-Point Methods (PDIPMs) are employed for solving large-scale SDPs, most of the computation time is occupied by the computation related to the Schur Complement Matrix (SCM). We have developed SDPARA (SemiDeflnite Programming Algorithm paRAllel version) to deal with such largescale SDPs. In particular, the latest version of SDPARA can handle sparse SCMs adequately. In this paper, we concisely describe how parallel implementation of SDPARA shortens the computation time of the SCM and then discuss the latest implementation for sparse SCMs. Numerical results show that SDPARA achieves remarkable parallel scalability and enables us to solve large-scale SDPs from control theory.