Computable Error Bounds for Semidefinite Programming
Journal of Global Optimization
On Uniform Global Error Bounds for Convex Inequalities
Journal of Global Optimization
Stability of Error Bounds for Semi-infinite Convex Constraint Systems
SIAM Journal on Optimization
SIAM Journal on Optimization
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In 1952, A. J. Hoffman [J. Res. Natl. Bur. Standards, 49 (1952), pp. 263-2651] published a bound on the distance from any point to the solution set of a linear system. This bound subsequently has found applications in the sensitivity analysis of linear/integer programs and the convergence analysis of descent methods for linearly constrained minimization. A certain constant in Hoffman's bound may be interpreted as a condition number for the linear system and, in this paper, the authors give 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 vertex solutions proposed by J.-S. Pang.