An implementable active-set algorithm for computing a B-stationary point of a mathematical program with linear complementarity constraints (vol 12, pg 724, 2002)

摘要

In [M. Fukushima and P. Tseng, SIAM J. Optim., 12 ( 2002), pp. 724 - 739], an epsilon-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 epsilon-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.