Error bounds for convex differentiable inequality systems in Banach spaces

The paper is devoted to studying the Hoffman global error bound for convex quadratic/affine inequality/equality systems in the context of Banach spaces. We prove that the global error bound holds if the Hoffman local error bound is satisfied for each subsystem at some point of the solution set of the system under consideration. This result is applied to establishing the equivalence between the Hoffman error bound and the Abadie qualification condition, as well as a general version of Wang &; Pang's result 30], on error bound of Hölderian type. The results in the present paper generalize and unify recent works by Luo &; Luo in 17], Li in 16] and Wang &; Pang in 30].