PERTURBATION ANALYSIS OF A CONDITION NUMBER FOR LINEAR-SYSTEMS

In 1952, A. J. Hoffman [J. Res. Natl. Bur. Standards, 49 (1952), pp. 2 63-265] published a bound on the distance from any point to the soluti on set of a linear system. This bound subsequently has found applicati ons in the sensitivity analysis of linear/integer programs and the con vergence analysis of descent methods for linearly constrained minimiza tion. A certain constant in Hoffman's bound may be interpreted as a co ndition number for the linear system and, tn this paper, the authors g ive simple necessary and sufficient conditions for the constant to be uniformly bounded under perturbations on the problem data. Also, these conditions are related to a uniform boundedness condition on the vert ex solutions proposed by J.-S. Pang.