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Arg max

The notation arg max (or argmax) in mathematical descriptions stands for the argument of the maximum, that is to say, the value of the given argument for which the value of the given expression attains its maximum value. This is well-defined only if the maximum is reached at a single value. Thus

holds if and only if x0 is the unique value of x for which f(x) is maximized.

arg min (or argmin) is defined analogously.