Error bounds for solutions of linear equations and inequalities

Given a system of linear equations and inequalities inn variables, a famous result due to A. J. Hoffman (1952) says that the distance of any point in ⁿ to the solution set of this system is bounded above by the product of a positive constant and the absolute residual. We shall discuss explicit representations of this constant in dependence upon the pair of norms used for the estimation. A method for computing a special form of Hoffman constants is proposed. Finally, we use these results in the analysis of Lipschitz continuity for solutions of parametric quadratic programs.