Probabilistic Analyses of the GCC Condition Number
In Chap. 6 we identified the GCC condition number as the crucial parameter in the perturbation theory of the polyhedral conic feasibility problem PCFP. Later on, we saw that this quantity occurs in cost estimates for an ellipsoid method finding feasible points in a nonempty cone and for interior-point methods deciding feasibility of polyhedral conic systems. Furthermore, the development in Chap. 10 showed that this condition number also plays a central role in cost estimates for deciding feasibility of primal–dual pairs in linear programming.
Continuing with one of the central themes in our exposition, we perform in this chapter probabilistic analyses of the GCC condition number, as was done in Chap. 2 for the condition number of linear equation solving. We obtain average and smoothed analysis estimates.