A Preconditioning Technique for Schur Complement Systems Arising in Stochastic Optimization

TitleA Preconditioning Technique for Schur Complement Systems Arising in Stochastic Optimization
Publication TypeJournal Article
Year of Publication2011
AuthorsPetra, CG, Anitescu, M
JournalComputational Optimization and Applications
Pagination1-30
Date Published06/2011
Abstract

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.

URLhttp://www.citeulike.org/article/9514087
PDFhttp://www.mcs.anl.gov/papers/P1748.pdf