An Implementable Active-Set Algorithm for Computing a B-Stationary Point of a Mathematical Program with Linear Complementarity Constraints: Erratum

In [3], an 2-active set algorithm was proposed for solving a mathematical program with a smooth objective function and linear inequality/complementarity constraints. It is asserted therein that, under a uniform LICQ on the 2-feasible set, this algorithm generates iterates whose cluster points are B-stationary points of the problem. However, the proof has a gap and only shows that each cluster point is an M-stationary point. We discuss this gap and show that B-stationarity can be achieved if the algorithm is modified and an additional error bound condition holds.