In
mathematics, maxima and minima, known collectively as extrema, are the largest value (maximum) or smallest value (minimum), that a
function takes in a point either within a given neighbourhood (local extremum) or on the function
domain in its entirety (global extremum).
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Local "valleys" or minor "dents" in a
loss function which, in many practical applications, will produce extremely large or small parameter estimates with very large
standard errors. The
Simplex method is particularly effective in avoiding such minima; therefore, this method may be particularly well suited in order to find appropriate start values for complex functions.
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