ArgMinUnique(f(x), x, P(x)) represents the unique point r
satisfying P(r)
such that f(r)=P(x)minf(x). This operation is only defined if such a unique point exists.
The argument x to this operator defines a locally bound variable. 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. More generally, x can be a collection of variables (x,y,…)
all of which become locally bound, with a corresponding predicate P(x,y,…).
Definitions:
| Fungrim symbol | Notation | Short description |
|---|---|---|
| ArgMinUnique | P(x)argmin*f(x) | Unique location of minimum value |
| Minimum | P(x)minf(x) | Minimum value of a set or function |
Source code for this entry:
Entry(ID("f4fbb8"),
SymbolDefinition(ArgMinUnique, ArgMinUnique(f(x), x, P(x)), "Unique location of minimum value"),
Description(SourceForm(ArgMinUnique(f(x), x, P(x))), "represents the unique point", r, "satisfying", P(r), "such that", Equal(f(r), Minimum(f(x), x, P(x))), ". This operation is only defined if such a unique point exists."),
Description("The argument", SourceForm(x), "to this operator defines a locally bound variable.", "The corresponding predicate", P(x), "must define the domain of", x, "unambiguously; that is, it must include a statement such as", Element(x, S), "where", S, "is a known set.", "More generally,", SourceForm(x), "can be a collection of variables", Tuple(x, y, Ellipsis), "all of which become locally bound, with a corresponding predicate", P(x, y, Ellipsis), "."))