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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.

MSC:

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

Citations:

Zbl 1005.65064
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