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 OptionsDetails 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, xIntegers can be used to specify that a variable can take on only integer values.
  • FindArgMin takes the same options as FindMinimum.

ExamplesExamplesopen allclose all

Basic Examples (3)Basic Examples (3)

Find a point at which the univariate function has a minimum:

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Find a point at which the function Sin[x]Sin[2y] has a minimum:

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Find a point at which a function is a minimum subject to constraints:

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