Hoffman's error bound, local controllability, and sensitivity analysis (vol 38, pg 947, 2000)

The proofs of Lemma 5.2 and Theorem 5.1 in [SIAM J. Control Optim., 38 (200 0), pp. 947-970] have a common error which concerns the existence of (local ly) Lipschitz selections. Indeed, Lemma 5.2 is true in the case where the m ultivalued mapping G is convex-valued, and in our case this assumption is n ot satisfied. So some modifications are needed. The statement of Theorem 5. 1 (which does not use Lemma 5.2) is as follows.