The inexact SQP method which we describe in Chapter 5 requires first and second order derivatives of the problem functions. There are several ways how derivatives can be provided. The first is to have them provided along with the problemdependent model functions by the user. This can be cumbersome for the user and it is impossible for the program to check whether the derivatives are free of errors, even though consistency tests evaluated in a few points can somewhat mitigate the problem. These are, however, severe drawbacks.
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