A parallel interior-point algorithm for linear programming on a shared memory machine

Erling D. Andersen and Knud D. Andersen

The XPRESS interior point optimizer is an ``industrial strength'' code for solution of large-scale sparse linear programs. The purpose of the present paper is to discuss how the XPRESS interior p oint optimizer has been parallelized for a Silicon Graphics multi processor computer. The major computational task, performed in each iteration of the interior-point method implemented in the XPRESS interior point optimizer is the solution of a symmetric and positive definite system of linear equations. Therefore, parallelization of the Cholesky decomposition and the triangular solve procedure are discussed in detail. Finally, computational results are presented to demonstrate the parallel efficiency of the optimizer. It should be emphasized that the methods discussed can be applied to the solution of large-scale sparse linear least squares problems.

CORE Discussion Paper 9808, CORE, Louvain-La-Neuve, Belgium, 1998.

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