Local vs. global optima

There are three prevailing reasons to try and locate the true global optimum. In the first place, if an analysis needs to be performed a great number of times (e.g. in process monitoring, quality control), then it will be rewarding to spend time and effort on the optimization, in order that the analysis can be run quickly and cheaply on a routine basis. If the expected number of analyses to be run is small, then it is only necessary to reach sufficient resolution for all components in a reasonable time. 

The third reason is that a procedure cannot be designed to find the global optimum only when it matters. In a number of cases we may give credit to an optimization procedure for yielding a satisfactory result, even if this result is a local optimum only. However, we cannot expect the same procedure to yield a satisfactory result in a case in which the global optimum is the only one at which an acceptable separation may be achieved. 

We may conclude that local optima may be more acceptable as a result 

the fewer the number of analyses that will have to be run on the optimized system, 

the more information we have about the entire response surface, and 

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