Error Bounds for Lower Semicontinuous Functions in Normed Spaces

Abstract

Without the convexity or analyticity assumption, we study error bounds for an inequality system defined by a general lower semicontinuous function and establish sufficient/necessary conditions on the existence of error bounds in infinite dimensional normed spaces. Some characterizations for a convex inequality system to possess an error bound in a reflexive Banach space are also given. As applications, in dealing with the Hoffman error bound result in normed spaces, we give a computable Lipschitz bound constant, which is better than previous Lipschitz bound constants in some examples; we also consider error bounds for quadratic functions on Rn.