The global convergence of augmented Lagrangian methods based on NCP function in constrained nonconvex optimization

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In this paper, we present the global convergence properties of the primal–dual method using a class of augmented Lagrangian functions based on NCP function for inequality constrained nonconvex optimization problems. We construct four modified augmented Lagrangian methods based on different algorithmic strategies. We show that the convergence to a KKT point or a degenerate point of the original problem can be ensured without requiring the boundedness condition of the multiplier sequence.