Interior-Point Abstracts

Presolve Analysis of Linear Programs Prior to Applying an Interior Point Method

Jacek Gondzio

Several issues concerning an analysis of large and sparse linear programming problems prior to solving them with an interior point based optimizer are addressed in this paper. Three types of presolve procedures are distinguished. Routines from the first class repeatedly analyze an LP problem formulation: eliminate empty or singleton rows and columns, look for primal and dual forcing or dominated constraints, tighten bounds for variables and shadow prices or just the opposite, relax them to find implied free variables. The second type of analysis aims at reducing a fill-in of the Cholesky factor of the normal equations matrix used to compute orthogonal projections and includes a heuristic for increasing the sparsity of the LP constraint matrix and a technique of splitting dense columns in it. Finally, routines from the third class detect, and remove, different linear dependecies of rows and columns in a constraint matrix.

Computational results on problems from the Netlib collection, including some recently added infeasible ones, are given.

Technical Report 1994.3, Logilab, HEC Geneva, Section of Management Studies, University of Geneva, Bd. Carl-Vogt 102, 1211 Geneva, Switzerland, February 1994, revised December 1994.