Parallel implementation of a semidefinite programming solver based on CSDP on a distributed memory cluster

Authors:
I. D. Ivanov;E. de Klerk
Affiliations:
Faculty of Electrical Engineering, Mathematics and Computer Sciences, Delft University of Technology, Delft, GA, The Netherlands;Department of Econometrics and Operations Research, Tilburg University, Tilburg, The Netherlands
Venue:
Optimization Methods & Software - The 2nd Veszprem Optimization Conference: Advanced Algorithms (VOCAL), 13-15 December 2006, Veszprem, Hungary
Year:
2010

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Abstract

In this paper, we present the algorithmic framework and practical aspects of implementing a parallel version of a primal-dual semidefinite programming solver on a distributed memory computer cluster. Our implementation is based on the CSDP solver and uses a message passing interface and the ScaLAPACK library. A new feature is implemented to deal with problems that have rank-one constraint matrices. We show that significant improvement is obtained for a test set of problems with rank-one constraint matrices. Moreover, we show that very good parallel efficiency is obtained for large-scale problems where the number of linear equality constraints is very large compared to the block sizes of the positive semidefinite matrix variables.