Error bounds for nondifferentiable convex inequalities under a strong Slater constraint qualification

A global error bound is given on the distance between an arbitrary point in the n-dimensional real space R n and its projection on a nonempty convex set determined by m convex, possibly nondiierentiable, inequalities. The bound is in terms of a natural residual that measures the violations of the inequalities multiplied by a new simple condition constant that embodies a single strong Slater constraint qualiication (CQ) which implies the ordinary Slater CQ. A very simple bound on the distance to the projection relative to the distance to a point satisfying the ordinary Slater CQ is given rst and then used to derive the principal global error bound. Abbreviated Title. Error bounds under a strong Slater CQ