<s>
Mehrotra	O
's	O
predictor	O
–	O
corrector	O
method	O
in	O
optimization	O
is	O
a	O
specific	O
interior	B-Algorithm
point	I-Algorithm
method	I-Algorithm
for	O
linear	B-Algorithm
programming	I-Algorithm
.	O
</s>
<s>
The	O
method	O
is	O
based	O
on	O
the	O
fact	O
that	O
at	O
each	O
iteration	B-Algorithm
of	O
an	O
interior	O
point	O
algorithm	O
it	O
is	O
necessary	O
to	O
compute	O
the	O
Cholesky	O
decomposition	O
(	O
factorization	O
)	O
of	O
a	O
large	O
matrix	O
to	O
find	O
the	O
search	O
direction	O
.	O
</s>
<s>
At	O
each	O
iteration	B-Algorithm
of	O
the	O
algorithm	O
,	O
Mehrotra	O
's	O
predictor	O
–	O
corrector	O
method	O
uses	O
the	O
same	O
Cholesky	O
decomposition	O
to	O
find	O
two	O
different	O
directions	O
:	O
a	O
predictor	O
and	O
a	O
corrector	O
.	O
</s>
<s>
However	O
,	O
the	O
additional	O
overhead	O
per	O
iteration	B-Algorithm
is	O
usually	O
paid	O
off	O
by	O
a	O
reduction	O
in	O
the	O
number	O
of	O
iterations	B-Algorithm
needed	O
to	O
reach	O
an	O
optimal	O
solution	O
.	O
</s>
<s>
The	O
average	O
value	O
of	O
the	O
products	O
constitute	O
an	O
important	O
measure	O
of	O
the	O
desirability	O
of	O
a	O
certain	O
set	O
(	O
the	O
superscripts	O
denote	O
the	O
value	O
of	O
the	O
iteration	B-Algorithm
number	O
,	O
,	O
of	O
the	O
method	O
)	O
.	O
</s>
<s>
Secondly	O
,	O
it	O
solves	O
the	O
aggregated	O
system	O
to	O
obtain	O
the	O
search	O
direction	O
of	O
the	O
current	O
iteration	B-Algorithm
.	O
</s>
<s>
Here	O
,	O
is	O
the	O
duality	O
measure	O
of	O
the	O
affine	O
step	O
and	O
is	O
the	O
duality	O
measure	O
of	O
the	O
previous	O
iteration	B-Algorithm
.	O
</s>
<s>
Although	O
the	O
modifications	O
presented	O
by	O
Mehrotra	O
were	O
intended	O
for	O
interior	O
point	O
algorithms	O
for	O
linear	B-Algorithm
programming	I-Algorithm
,	O
the	O
ideas	O
have	O
been	O
extended	O
and	O
successfully	O
applied	O
to	O
quadratic	B-Algorithm
programming	I-Algorithm
as	O
well	O
.	O
</s>
