Computation of condition numbers for linear programming problems using Penas method

We present the computation of the condition numbers for linear programming (LP) problems from the NETLIB suite. The method of Pena [Pena, J., 1998, {Computing the distance to infeasibility: theoretical and practical issues}. Technical report, Center for Applied Mathematics, Cornell University.] was used to compute the bounds on the distance to ill-posedness rho(d) of a given problem instance with data d , and the condition number was computed as C (d) = parallel to d parallel to/rho(d ). We discuss the efficient implementation of Pena's method and compare the tightness of the estimates on C(d) computed by Pena's method to that computed by the method employed by Ordonez and Freund [Ordonez, F. and Freund, R.M., 2003, {Computational experience and the explanatory value of condition measures for linear optimization}. SIAM Journal on Optimization, 14, 307-333.]. While Pena's method is generally much cheaper, the bounds provided are generally not as tight as those computed by Ordonez and Freund. As a by-product, we use the computational results to study the correlation between log C(d) and the number of interior-point method 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 Ordonez and Freund.