<s>
In	O
mathematics	O
,	O
specifically	O
functional	B-Application
analysis	I-Application
,	O
the	O
barrier	B-Algorithm
cone	I-Algorithm
is	O
a	O
cone	O
associated	O
to	O
any	O
non-empty	O
subset	O
of	O
a	O
Banach	O
space	O
.	O
</s>
<s>
It	O
is	O
closely	O
related	O
to	O
the	O
notions	O
of	O
support	O
functions	O
and	O
polar	B-Algorithm
sets	I-Algorithm
.	O
</s>
<s>
defined	O
for	O
each	O
continuous	O
linear	O
functional	O
ℓ	O
on	O
X	O
,	O
is	O
known	O
as	O
the	O
support	O
function	O
of	O
the	O
set	O
K	O
;	O
thus	O
,	O
the	O
barrier	B-Algorithm
cone	I-Algorithm
of	O
K	O
is	O
precisely	O
the	O
set	O
of	O
continuous	O
linear	O
functionals	O
ℓ	O
for	O
which	O
σK(ℓ )	O
is	O
finite	O
.	O
</s>
<s>
The	O
set	O
of	O
continuous	O
linear	O
functionals	O
ℓ	O
for	O
which	O
σK(ℓ )	O
≤1	O
is	O
known	O
as	O
the	O
polar	B-Algorithm
set	I-Algorithm
of	O
K	O
.	O
The	O
set	O
of	O
continuous	O
linear	O
functionals	O
ℓ	O
for	O
which	O
σK(ℓ )	O
≤0	O
is	O
known	O
as	O
the	O
(	O
negative	O
)	O
polar	O
cone	O
of	O
K	O
.	O
Clearly	O
,	O
both	O
the	O
polar	B-Algorithm
set	I-Algorithm
and	O
the	O
negative	O
polar	O
cone	O
are	O
subsets	O
of	O
the	O
barrier	B-Algorithm
cone	I-Algorithm
.	O
</s>
