Erratum to: Nonlinear programming without a penalty function or a filter

This note reports a correction to the results obtained by [2], in which an error was unfortunately discovered during work with D. Robinson. The problem is in the proof of Lemma 3.10 of this reference, where it is claimed that Lemma 6.5.3 of [1] can be invoked to deduce that ρc k ≥ η2, where ρc k is a specific ratio of achieved to predicted reduction is constraint violation and η2 is a constant in (0, 1). As it turns out, the reasoning is only correct if the ratio ‖sk‖/ ∥ ∥s R k ∥ ∥ is bounded above, where sk is the step at iteration k and s R k is its projection onto the range of the transposed Jacobian J T k . Handling the case where this ratio is unbounded above turned out to be surprisingly complex. In particular, this required considering separately the cases where the tangential component of the step at iteration k is large or small with respect to its normal component, where the meaning of “large” and “small” has to be defined very specifically. The convergence proof taking this distinction into account is therefore significantly more involved than the proof of [2], and cannot be presented in the form of a few corrections in the original text. The report [4] (including substantial contribution by D. Robinson) proposes a corrected version of [2], where other minor