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NArgMax

NArgMax[f, x]
gives a position x_max at which f is numerically maximized.

NArgMax[f, {x, y, ...}]
gives a position {x_max, y_max, ...} at which f is numerically maximized.

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

NArgMax[..., {x, y, ...}] is effectively equivalent to {x, y, ...}/.Last[NMaximize[..., {x, y, ...}, ...].

NArgMax always attempts to find a global maximum 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, NArgMax can always find global maxima, over both real and integer values.

If NArgMax determines that the constraints cannot be satisfied, it returns {Indeterminate, ...}.

Find a maximizer point for a univariate function:

Find a maximizer point for a multivariate function:

Find a maximizer point for a function subject to constraints:

Find a maximizer point for a univariate function:

Find a maximizer point for a multivariate function:

Find a maximizer point for a function subject to constraints:

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

NMaximize gives both the value of the maximum and the maximizer point:

NArgMax gives the maximizer point:

NMaxValue gives the maximum:

The objective function may be unbounded:

There may be no points satisfying the constraints: