Constraints generic iteration

In a generic iteration, a feasible point is known together with the active variable bounds and inequality constraints. If the point is anything other than solution, a search direction must be determined to improve the objective function. In this search, all the active inequality constraints are treated as equality constraints, whereas the active bounds are used to simplify the problem. 

In a generic iteration, Xj used in the function (12.23), can be quite different from the exact ones, especially when many constraints are present. Thus, the Maratos effect could occur. 

If the search is performed for an object from the lower levels, it is useful to limit the number of its iterations. For instance, suppose we want to solve a problem of maximum level that is a generic objective function bounds, linear, nonlinear equality and inequality constraints. The search for a new point that is better than the previous one can be performed with different strategies that can be used sequentially or in parallel, as required. The most important are the following ... 

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