Error Bounds for Nondifferentiable Convex Inequalities under a Strong Slater Constraint Qualification
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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 nondifferentiable, 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 qualification (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 first and then used to derive the principal global error bound.
Strong Slater constraint qualification