ERROR-BOUNDS FOR NONDIFFERENTIABLE CONVEX INEQUALITIES UNDER A STRONGSLATER CONSTRAINT QUALIFICATION

A global error bound is given on the distance between an arbitrary poi nt in the n-dimensional real space R-n and its projection on a nonempt y convex set determined by m convex, possibly nondifferentiable, inequ alities. The bound is in terms of a natural residual that measures the violations of the inequalities multiplied by a new simple condition c onstant 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 satisfy ing the ordinary Slater CQ is given first and then used to derive the principal global error bound. (C) 1998 The Mathematical Programming So ciety, Inc. Published by Elsevier Science B,V.