The APOS linear programming solver: an implementation of the homogeneous algorithm

Erling D. Andersen and Knud D. Andersen
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Erling D. Andersen: Department of Management, Odense University, Denmark
Knud D. Andersen: Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium

No 1997030, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: The purpose of this work is to present the APOS linear programming (LP) solver intended for solution of large-scale sparse LP problems. The solver is based on the homogeneous interior- point algorithm which in contrast to the primal-dual algorithm detects a possible primal or dual infeasibility reliably. It employs advanced (parallelized) linear algebra, it handles dense columns in the constraint matrix efficiently, and it has a basis identification procedure. Moreover, recently the solver has been incorporated into the commercially available XPRESS-MP software. This paper discusses in details the algorithm and linear algebra employed by the APOS LP solver. In particular the homogeneous algorithm is emphasized. Furthermore, extensive com- putational results are reported. These results include comparative results for the XPRESS-MP simplex and barrier code and the freely available BPMPD code developed by Cs. M?esz?aros. Finally, computational results are presented to demonstrate the possible speed-up, when using a parallelized version of the APOS LP solver on a Silicon Graphics Challenge computer.

Date: 1997-04-01
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