Prediction techniques constraint refinement

One important class of nonlinear programming techniques is called quadratic programming (QP), where the objective function is quadratic and the constraints are linear. While the solution is iterative, it can be obtained quickly as in linear programming. This is the basis for the newest type of constrained multivariable control algorithms called model predictive control, which is heavily used in the refining industry. See the earlier subsection on model predictive control for more details. 

Applications of spectrum prediction to the evaluation of candidate structures have some special requirements. First, comparisons are to be between predicted and experimental spectra, not relative comparisons between predicted spectra therefore, the predicted spectrum of a compound must closely approximate its experimentally determined spectrum. Second, the methods must be applicable to larger, complex, highly functionalized compounds as well as smaller, simpler ones. Third, spectrum prediction must be sufficiently refined to yield spectral distinctions between isomeric compounds that possess structural similarities (structural building units and constraints), which at times can be substantial. If they are to be of value, the techniques should be more discriminating than those used in spectrum interpretation. Finally, since at times there may be many structures whose spectral properties are to be predicted, the methods should be computationally efficient. 

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