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BUILT-IN MATHEMATICA SYMBOL
FindArgMin
FindArgMin[f, x]
gives the position 
of a local minimum of f.
FindArgMin[f, {x, x0}]
gives the position 
of a local minimum of f, found by a search starting from the point 
.
FindArgMin[f, {{x, x0}, {y, y0}, ...}]
gives the position 
of a local minimum of a function of several variables.
FindArgMin[{f, cons}, {{x, x0}, {y, y0}, ...}]
gives the position of a local minimum subject to the constraints cons.
FindArgMin[{f, cons}, {x, y, ...}]
starts from a point within the region defined by the constraints.
Details and Options
- FindArgMin[..., {x, y, ...}] is effectively equivalent to {x, y, ...}/.Last[FindMinimum[..., {x, y, ...}, ...].
- If the starting point for a variable is given as a list, the values of the variable are taken to be lists with the same dimensions.
- cons can contain equations, inequalities or logical combinations of these.
- FindArgMin first localizes the values of all variables, then evaluates f with the variables being symbolic, and then repeatedly evaluates the result numerically.
- FindArgMin has attribute HoldAll, and effectively uses Block to localize variables.
- FindArgMin[f, {x, x0, x1}] searches for a local minimum in f using
and 
as the first two values of x, avoiding the use of derivatives. - FindArgMin[f, {x, x0, xmin, xmax}] searches for a local minimum, stopping the search if x ever gets outside the range
to 
. - Except when f and cons are both linear, the results found by FindArgMin may correspond only to local, but not global, minima.
- By default, all variables are assumed to be real.
- For linear f and cons, x
Integers can be used to specify that a variable can take on only integer values. - FindArgMin takes the same options as FindMinimum.
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