**Definition. **A set is said to be *concave* if for every
vector and in ,
is in for
all
. In other words, all points on the line between two points
of lie in .

**Definition. **A *functional* is a mapping from a vector space to the
real numbers .

Thus, for example, every *norm* is a functional.

**Definition. **A *linear functional* is a functional such that
for each and in the linear space , and for all scalars
and , we have
.

**Definition. **The *norm of a linear functional* is defined on
the normed linear space by

**Definition. **A functional defined on a concave subset of a vector space
is said to be *concave* on if for
every vector and in ,

**Definition. **A *local minimizer* of a real-valued function is
any such that
in some neighborhood of .

**Definition. **A *global minimizer* of a real-valued function
on a set
is
any
such that
for all .

**Definition. **A *cluster point* of a sequence is any point
such that every neighborhood of contains at least one .

**Definition. **The *concave hull* of a set in a metric space is the
smallest concave set containing .

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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