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

E. D. Andersen and K. D. Andersen

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{Available from Dash Associates, see} 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 computational 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.

CORE, Universite Catholique de Louvain, CORE discussion paper #9337, 1997.