ArgMax(f(x), ForElement(x, S)), rendered x∈Sargmaxf(x), gives the set of values x∈S
such that f(x)=s∈Smaxf(s).
ArgMax(f(x), ForElement(x, S), P(x)), rendered x∈S,P(x)argmaxf(x), gives the set of values x∈S
satisfying P(x)
and such that f(x)=s∈S,P(s)maxf(s).
If f(x)
does not attain a maximum value satisfying the conditions, the result is the empty set {}.
ArgMax(f(x, y), For(Tuple(x, y)), P(x, y)), rendered P(x,y)argmaxf(x,y), gives the set of tuples (x,y)
satisfying P(x,y)
such that f(x,y)=P(s,t)maxf(s,t), and similarly for any number n≥2
of variables.
The special expression For(x) or ForElement(x, S) declares x as a locally bound variable within the scope of the arguments to this operator. If For(x) is used instead of ForElement(x, S), the corresponding predicate P(x)
must define the domain of x
unambiguously; that is, it must include a statement such as x∈S
where S
is a known set. Similarly, For(Tuple(x, y)), For(Tuple(x, y, z)), etc. defines multiple locally bound variables which must be accompanied by a multivariate predicate P(x,y), P(x,y,z), etc.
Definitions:
Fungrim symbol | Notation | Short description |
---|---|---|
ArgMax | x∈Sargmaxf(x) | Locations of maximum value |
Maximum | x∈Smaxf(x) | Maximum value of a set or function |
Source code for this entry:
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