Abstract
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 ℝn 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.
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Klatte, D., Thiere, G. Error bounds for solutions of linear equations and inequalities. ZOR - Mathematical Methods of Operations Research 41, 191–214 (1995). https://doi.org/10.1007/BF01432655
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DOI: https://doi.org/10.1007/BF01432655