Variations of the Nelder-Mead direct search method are employed to find read channel parameter settings in a discrete field having three or more dimensions. The three or more dimensions correspond to read channel parameters, at least some of which are highly correlated. The steps of the Nelder-Mead method are executed according to a methodology to arrive at substantially optimal parameter settings for a read channel, even where a discrete function defining parameter outcomes is noisy. In some embodiments, dimensional collapse, considered inefficient in a two-dimensional field, is allowed in order to reach an optimal solution in a greater-than-two-dimensional field.