Deterministic sample average approximations of stochastic programming problems with recourse are suitable for a scenario-based, treelike parallelization with interior-point methods and a Schur complement mechanism. However, the direct linear solves involving the Schur complement matrix are expensive, and adversely a ect the scalability of this approach. In this paper we propose a stochastic preconditioner to address this issue. The spectral analysis of the preconditioned matrix indicates an ex- ponential clustering of the eigenvalues around 1. The numerical experiments performed on the relaxation of a unit commitment problem show good performance, in terms of both the accuracy of the solution and the execution time.
Citation
Preprint ANL/MCS-P1748-0510, Argonne National Laboratory, Argonne, IL, May 2010.
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View A preconditioning technique for Schur complement systems arising in stochastic optimization