%A O. L. Mangasarian
%T Error Bounds for Nondifferentiable Convex Inequalities under a Strong Slater Constraint Qualification
%D July 1996 -- Revised March 1997
%R 96-04
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X 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 of 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.