Erratum to: Inexact constraint preconditioners for linear systems arising in interior point methods

It was brought to our attention by Professor Valeria Simoncini that our proof of Theorem 2.1 [2, p. 139] is incorrect. Indeed, on page 140 we write the inequality (2.4) which is correct because we work with à which is an m× n matrix and m ≤ n and rank(A)=m hence ‖ÃT y‖ ‖y‖ ≥ σ̃1. However, on page 141 we write the inequality (2.6). We try to use a similar argument but now instead of à we have à and x ∈Rn. Hence the inequality ‖Ãx‖ ‖x‖ ≥ σ̃1 (which we use to prove inequality (2.6)) is incorrect. In this short note we restate Theorem 2.1 of [2] and give a new proof.