ArgMin

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

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

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

Examples

Find where a function is minimized:

ArgMin[x^2 + 2x + 1, x]
(* -1 *)

With constraints:

ArgMin[{x^2 + y^2, x + y == 1}, {x, y}]
(* {1/2, 1/2} *)

Please visit the official Wolfram Language Reference for more details.