Built-in Mathematica Symbol

FindArgMin

FindArgMin[f, x]
gives the position x_min of a local minimum of f.

FindArgMin[f, {x, x₀}]
gives the position x_min of a local minimum of f, found by a search starting from the point x=x₀.

FindArgMin[f, {{x, x₀}, {y, y₀}, ...}]
gives the position {x_min, y_min, ...} 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.

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.

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 x₀ and x₁ as the first two values of x, avoiding the use of derivatives.

FindArgMin[f, {x, x₀, x_min, x_max}] searches for a local minimum, stopping the search if x ever gets outside the range x_min to x_max.

Except when f and cons are both linear, the results found by FindArgMin may correspond only to local, but not global, minima.

For linear f and cons, xIntegers can be used to specify that a variable can take on only integer values.

Find a point {x} at which the univariate function 2x^2+3x-5 has a minimum:

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

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