"A Preconditioning Technique for Schur Complement Systems Arising in Stochastic Optimization"
C. G. Petra and M. Anitescu
Computational Optimization and Applications, , pp. 1-30.
Preprint Version: [pdf]
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 affect 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 exponential 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.