An Implementable Active‐Set Algorithm for Computing a B‐Stationary Point of a Mathematical Program with Linear Complementarity Constraints: Erratum - Fukushima, Masao; Tseng, Paul (SIAM journal on optimization, 2007)
In [M. Fukushima and P. Tseng, SIAM J. Optim., 12 (2002), pp. 724-739], an ε-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 ε-feasible set, this algorithm generates iterates whose cluster points are B-stationary points of the problem. However, the proof has a gap and shows only 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.