Fungrim entry: f4fbb8

Symbol: ArgMinUnique —

\mathop{\operatorname{arg\,min*}}\limits_{P\left(x\right)} f\!\left(x\right)

— Unique location of minimum value

ArgMinUnique(f(x), x, P(x)) represents the unique point

r

satisfying

P\!\left(r\right)

such that

f\!\left(r\right) = \mathop{\min}\limits_{P\left(x\right)} f\!\left(x\right)

. 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\!\left(x\right)

must define the domain of

x

unambiguously; that is, it must include a statement such as

x \in S

where

S

is a known set. More generally, x can be a collection of variables

\left(x, y, \ldots\right)

all of which become locally bound, with a corresponding predicate

P\!\left(x, y, \ldots\right)

Definitions:

Fungrim symbol	Notation	Short description
`ArgMinUnique`	$\mathop{\operatorname{arg\,min*}}\limits_{P\left(x\right)} f\!\left(x\right)$	Unique location of minimum value
`Minimum`	$\mathop{\min}\limits_{P\left(x\right)} f\!\left(x\right)$	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), "."))

Topics using this entry

Operators