Macromolecular structures optimization problem

Optimization problems in crystallographic structure refinement are seldom convex, that is very rarely characterized by a unimodal function/(x). Regularization of a two-atom model is an example of such a unimodal function. Fig. 11.2a. in contrast. Fig. 11.2b shows a profile of a function for modelling an amino acid side chain - the peaks correspond to the possible rotamers. In this case, the shape of the function/(x) is called multimodal. Such functions arise naturally in structural macromolecular optimization problems and possess a highly complex multiminima energy landscape that does not lend itself favourably to standard robust optimization techniques. 

With increased computer storage and speed, the feasible methods for solution of very large (e.g., O(105) or more variables) nonlinear optimization problems arising in important applications (macromolecular structure, meteorology, economics) will undoubtedly expand considerably and make possible new orders of resolution. 

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