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Noname manuscript No. (will be inserted by the editor)

Summary: Noname manuscript No.
(will be inserted by the editor)
A preconditioning technique for Schur complement
systems arising in stochastic optimization
Cosmin G. Petra Mihai Anitescu
Received: date / Accepted: date
Preprint ANL/MCS-P1748-0510
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 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
1 Introduction
Stochastic programming (SP) is concerned with solving optimization problems involv-


Source: Anitescu, Mihai - Mathematics and Computer Science Division, Argonne National Laboratory
Argonne National Laboratory, Mathematics and Computer Science Division (MCS)


Collections: Computer Technologies and Information Sciences; Mathematics