The Nonlinear Constraints Effect

The methods considered up to this point linearize the constraints when there are some nonlinearities. This can lead to some difficulties that any good program will 

Since the Hessian of the objective function is nonpositive definite, if we linearize the constraint and search for the minimum of the function (13.92), an unbounded problem is encountered with the linear constraint. 

One of the advantages of SQP methods is the modification of the objective function by also inserting the Hessian of the constraints into it. Thus, these methods somehow account for nonlinearities of constraints and often effectively solve problems with nonlinear constraints too. 

Another advantage of SQP methods is that they allow an alternative merit function to be used when the Maratos effect arises because of the nonlinearity of constraints. 

Nonlinear constraints can cause other problems when linearized, apart from the selected algorithm. 

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