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NArgMin

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

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

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

NArgMin[..., {x, y, ...}] is effectively equivalent to {x, y, ...}/.Last[NMinimize[..., {x, y, ...}, ...].

NArgMin always attempts to find a global minimum of f subject to the constraints given.

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

If f and cons are linear, NArgMin can always find global minima, over both real and integer values.

If NArgMin determines that the constraints cannot be satisfied, it returns {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 for a univariate function:

Find a minimizer point for a multivariate function:

Find a minimizer point for a function subject to constraints:

Find the lengths of sides of a unit area rectangle with minimal perimeter:

Find the lengths of sides of a unit area triangle with minimal perimeter:

NMinimize gives both the value of the minimum and the minimizer point:

NArgMin gives the minimizer point:

NMinValue gives the minimum:

The objective function may be unbounded:

There may be no points satisfying the constraints: