On Lagrange multipliers and constraints II. Augmented Lagrangian approach

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This paper establishes the relations between the changes in the values of the augmented multipliers and the changes in the values of the constraint and objective functions for a non-linear, non-convex programme based on the augmented Lagrangian which was introduced by one of the present authors. If the penalty parameters are sufficiently large, the monotonic relations hold between the augmented multipliers and the constraint functions near the optimal solution. Illustrative examples show that the classical Lagrangian fails to give rise to the relations for a. non-convex programme.