Optimization Online


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

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society