Built-in Mathematica Symbol

ArgMin

ArgMin[f, x]
gives a position x_min at which f is minimized.

ArgMin[f, {x, y, ...}]
gives a position {x_min, y_min, ...} at which f is minimized.

ArgMin[{f, cons}, {x, y, ...}]
gives a position at which f is minimized subject to the constraints cons.

ArgMin[{f, cons}, {x, y, ...}, dom]
gives a position at which f is minimized over the domain dom, typically Reals or Integers.

ArgMin[..., {x, y, ...}, ...] is effectively equivalent to {x, y, ...}/.Last[Minimize[..., {x, y, ...}, ...].

If f and cons are linear or polynomial, ArgMin will always find a global minimum.

If ArgMin is given an expression containing approximate numbers, it automatically calls NArgMin.

If the minimum is achieved only infinitesimally outside the region defined by the constraints, or only asymptotically, ArgMin will return the closest specifiable point.

xIntegers can be used to specify that a particular variable can take on only integer values.

If the constraints cannot be satisfied, ArgMin returns {Indeterminate, Indeterminate, ...}.

Find a minimizer point for a univariate function:

Find a minimizer point for a multivariate function:

Find a minimizer point for a function subject to constraints:

Find a minimizer point as a function of parameters: