A Parallel Block Cholesky Factorization for Staircase Linear Programming Problems

Etienne Loute and Jean-Philippe Vial
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Etienne Loute: Facultés Universitaires Saint-Louis, Brussels and CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
Jean-Philippe Vial: Département COMIN, Université de Genève, Switzerland

No 1992060, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: We present a variant of the Cholesky factorization for block tridiagonal positive definite matrices. We show that a suitable ordering of block pivots makes it possible to parallelize the linear algebra on a multiple instruction multiple data (MIMD) processor achitecture. The technique applies to linear programming problems with a staircase constraint matrix, a structure that is typical of dynamic (multiperiod, multistage) problems. We compute the amount of parallelism that is theoretically achievable and we show that the increase in block fill-in of the Cholesky factor is limited.

Keywords: Cholesky factorization; Parallelism; Block elimination; Staircase structure; Interior-point method (search for similar items in EconPapers)
Date: 1992-11-01
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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:1992060

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