An implementable active-set algorithm for computing a B-stationary point of a mathematical program with linear complementarity constraints: Erratum. (English) Zbl 1127.65034

Summary: M. Fukushima and P. Tseng [SIAM J. Optim. 12, No. 3, 724–739 (2002; Zbl 1005.65064)] have proposed an \(\varepsilon\)-active set algorithm 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 \(\varepsilon\)-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.


65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)


Zbl 1005.65064
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