<s>
Graduated	B-Algorithm
optimization	I-Algorithm
is	O
a	O
global	O
optimization	O
technique	O
that	O
attempts	O
to	O
solve	O
a	O
difficult	O
optimization	O
problem	O
by	O
initially	O
solving	O
a	O
greatly	O
simplified	O
problem	O
,	O
and	O
progressively	O
transforming	O
that	O
problem	O
(	O
while	O
optimizing	O
)	O
until	O
it	O
is	O
equivalent	O
to	O
the	O
difficult	O
optimization	O
problem	O
.	O
</s>
<s>
Graduated	B-Algorithm
optimization	I-Algorithm
is	O
an	O
improvement	O
to	O
hill	B-Algorithm
climbing	I-Algorithm
that	O
enables	O
a	O
hill	O
climber	O
to	O
avoid	O
settling	O
into	O
local	O
optima	O
.	O
</s>
<s>
Often	O
,	O
graduated	B-Algorithm
optimization	I-Algorithm
gives	O
better	O
results	O
than	O
simple	O
hill	B-Algorithm
climbing	I-Algorithm
.	O
</s>
<s>
Often	O
,	O
graduated	B-Algorithm
optimization	I-Algorithm
yields	O
good	O
results	O
even	O
when	O
the	O
sequence	O
of	O
problems	O
cannot	O
be	O
proven	O
to	O
strictly	O
meet	O
all	O
of	O
these	O
conditions	O
.	O
</s>
<s>
Graduated	B-Algorithm
optimization	I-Algorithm
is	O
commonly	O
used	O
in	O
image	O
processing	O
for	O
locating	O
objects	O
within	O
a	O
larger	O
image	O
.	O
</s>
<s>
Graduated	B-Algorithm
optimization	I-Algorithm
can	O
be	O
used	O
in	O
manifold	O
learning	O
.	O
</s>
<s>
The	O
Manifold	O
Sculpting	O
algorithm	O
,	O
for	O
example	O
,	O
uses	O
graduated	B-Algorithm
optimization	I-Algorithm
to	O
seek	O
a	O
manifold	O
embedding	O
for	O
non-linear	B-Algorithm
dimensionality	I-Algorithm
reduction	I-Algorithm
.	O
</s>
<s>
Simulated	B-Algorithm
annealing	I-Algorithm
is	O
closely	O
related	O
to	O
graduated	B-Algorithm
optimization	I-Algorithm
.	O
</s>
<s>
Instead	O
of	O
smoothing	O
the	O
function	O
over	O
which	O
it	O
is	O
optimizing	O
,	O
simulated	B-Algorithm
annealing	I-Algorithm
randomly	O
perturbs	O
the	O
current	O
solution	O
by	O
a	O
decaying	O
amount	O
,	O
which	O
may	O
have	O
a	O
similar	O
effect	O
.	O
</s>
<s>
Because	O
simulated	B-Algorithm
annealing	I-Algorithm
relies	O
on	O
random	O
sampling	O
to	O
find	O
improvements	O
,	O
however	O
,	O
its	O
computation	O
complexity	O
is	O
exponential	O
in	O
the	O
number	O
of	O
dimensions	O
being	O
optimized	O
.	O
</s>
<s>
By	O
contrast	O
,	O
graduated	B-Algorithm
optimization	I-Algorithm
smooths	O
the	O
function	O
being	O
optimized	O
,	O
so	O
local	O
optimization	O
techniques	O
that	O
are	O
efficient	O
in	O
high-dimensional	O
space	O
(	O
such	O
as	O
gradient-based	O
techniques	O
,	O
hill	O
climbers	O
,	O
etc	O
.	O
)	O
</s>
