Selection of the Merit Function

As above, the SQP method is not iterated without controls, but a merit function of Chapter 12 is usually adopted (for instance, i or the augmented Lagrangian penalty Junction alpf) to deem whether the iterations converge to the solution. 

Unfortunately, the so alled Maratos effect could arise if this strategy only is 

The Maratos effect was detected by applying the iterations of the SQP method to certain problems. This effect should not be surprising because only one function is used to reconcile two distinct problems minimizing the real function and solving the system of constraints. If the constraints are nonlinear, it may be impossible to reconcile these two problems in one function only. 

Despite considering the equations (13.72)-(13.75) only from the second viewpoint (as the iteration generated during the solution of a quadratic problem), it may be opportune to also account for the first viewpoint (the correction of the working point comes from an iteration of Newton s method applied to a nonlinear system). 

This alternative viewpoint, which is not antithetic with respect to the previous one, is adopted in the BzzConstrainedMinimization dass. 

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