Examples of "argmax"
are points "x" for which "f"("x") attains its smallest value. The complementary operator is argmax.
Note that formula_18 does not need to appear in the latter expression, as it's non-negative and independent of formula_19 and thus does not affect the argmax.
arg min and arg max are sometimes also written argmin and argmax, and stand for argument of the minimum and argument of the maximum.
In practice, finding the argmax over GEN(x) will be done using an algorithm such as Viterbi or an algorithm such as max-sum, rather than an exhaustive search through an exponentially large set of candidates.
In mathematics, the arguments of the maxima (abbreviated arg max or argmax) are the points of the domain of some function at which the function values are maximized. In contrast to global maxima, referring to the largest "outputs" of a function, arg max refers to the "inputs", or arguments, at which the function outputs are as large as possible.
These direct definition, especially the last, are rather unwieldy. For example, the argmax construction is artificial from the perspective of empirical measurements, when with a Weathervane or similar one can easily deduce the direction of flux at a point. Rather than defining the vector flux directly, it is often more intuitive to state some properties about it. Furthermore, from these properties the flux can uniquely be determined anyway.