<s>
In	O
mathematical	O
optimization	O
,	O
the	O
active-set	B-Algorithm
method	I-Algorithm
is	O
an	O
algorithm	O
used	O
to	O
identify	O
the	O
active	B-Algorithm
constraints	I-Algorithm
in	O
a	O
set	O
of	O
inequality	B-Application
constraints	I-Application
.	O
</s>
<s>
The	O
active	B-Algorithm
constraints	I-Algorithm
are	O
then	O
expressed	O
as	O
equality	O
constraints	B-Application
,	O
thereby	O
transforming	O
an	O
inequality-constrained	O
problem	O
into	O
a	O
simpler	O
equality-constrained	O
subproblem	O
.	O
</s>
<s>
is	O
called	O
active	O
at	O
if	O
,	O
and	O
inactive	O
at	O
if	O
Equality	O
constraints	B-Application
are	O
always	O
active	O
.	O
</s>
<s>
The	O
active	B-Algorithm
set	I-Algorithm
at	O
is	O
made	O
up	O
of	O
those	O
constraints	B-Application
that	O
are	O
active	O
at	O
the	O
current	O
point	O
.	O
</s>
<s>
The	O
active	B-Algorithm
set	I-Algorithm
is	O
particularly	O
important	O
in	O
optimization	O
theory	O
,	O
as	O
it	O
determines	O
which	O
constraints	B-Application
will	O
influence	O
the	O
final	O
result	O
of	O
optimization	O
.	O
</s>
<s>
For	O
example	O
,	O
in	O
solving	O
the	O
linear	B-Algorithm
programming	I-Algorithm
problem	I-Algorithm
,	O
the	O
active	B-Algorithm
set	I-Algorithm
gives	O
the	O
hyperplanes	O
that	O
intersect	O
at	O
the	O
solution	O
point	O
.	O
</s>
<s>
In	O
quadratic	B-Algorithm
programming	I-Algorithm
,	O
as	O
the	O
solution	O
is	O
not	O
necessarily	O
on	O
one	O
of	O
the	O
edges	O
of	O
the	O
bounding	O
polygon	O
,	O
an	O
estimation	O
of	O
the	O
active	B-Algorithm
set	I-Algorithm
gives	O
us	O
a	O
subset	O
of	O
inequalities	O
to	O
watch	O
while	O
searching	O
the	O
solution	O
,	O
which	O
reduces	O
the	O
complexity	O
of	O
the	O
search	O
.	O
</s>
<s>
Methods	O
that	O
can	O
be	O
described	O
as	O
active-set	B-Algorithm
methods	I-Algorithm
include	O
:	O
</s>
