Computation of condition numbers for linear programming problems using Peña's method

We present the computation of the condition numbers for linear programming (LP) problems from the NETLIB suite. The method of Peña [Technical report, Center for Applied Mathematics, Cornell University, May 1998] was used to compute the bounds on the distance to ill-posedness ρ(d) of a given problem instance with data d, and the condition number was computed as C(d) = ‖d‖/ρ(d). We discuss the efficient implementation of Peña’s method and compare the tightness of the estimates on C(d) computed by Peña’s method to that computed by the method employed by Ordóñez and Freund [SIAM J. Optimization, 14 (2003), pp. 307–333]. While Peña’s method is generally much cheaper, the bounds provided are generally not as tight as those computed by Ordóñez and Freund. As a by-product, we use the computational results to study the correlation between logC(d) and the number of IPM iterations taken to solve a LP problem instance. Our computational findings on the preprocessed problem instances from NETLIB suite are consistent with those reported by Ordóñez and Freund.