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A preconditioning technique for Schur complement systems arising in stochastic optimization

Cosmin Petra(petra***at***mcs.anl.gov)
Mihai Anitescu(anitescu***at***mcs.anl.gov)

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 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.

Keywords: stochastic programming; saddle-point preconditioning; Krylov methods; interior-point method; sample average approximations; parallel computing

Category 1: Stochastic Programming

Category 2: Optimization Software and Modeling Systems (Parallel Algorithms )

Citation: Preprint ANL/MCS-P1748-0510, Argonne National Laboratory, Argonne, IL, May 2010.

Download: [PDF]

Entry Submitted: 05/03/2010
Entry Accepted: 05/03/2010
Entry Last Modified: 05/03/2010

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