<s>
The	O
Nelder	B-Algorithm
–	I-Algorithm
Mead	I-Algorithm
method	I-Algorithm
(	O
also	O
downhill	B-Algorithm
simplex	I-Algorithm
method	I-Algorithm
,	O
amoeba	B-Algorithm
method	I-Algorithm
,	O
or	O
polytope	B-Algorithm
method	I-Algorithm
)	O
is	O
a	O
numerical	B-Algorithm
method	I-Algorithm
used	O
to	O
find	O
the	O
minimum	O
or	O
maximum	O
of	O
an	O
objective	O
function	O
in	O
a	O
multidimensional	O
space	O
.	O
</s>
<s>
It	O
is	O
a	O
direct	B-Algorithm
search	I-Algorithm
method	O
(	O
based	O
on	O
function	O
comparison	O
)	O
and	O
is	O
often	O
applied	O
to	O
nonlinear	O
optimization	O
problems	O
for	O
which	O
derivatives	O
may	O
not	O
be	O
known	O
.	O
</s>
<s>
However	O
,	O
the	O
Nelder	B-Algorithm
–	I-Algorithm
Mead	I-Algorithm
technique	O
is	O
a	O
heuristic	B-Algorithm
search	O
method	O
that	O
can	O
converge	O
to	O
non-stationary	O
points	O
on	O
problems	O
that	O
can	O
be	O
solved	O
by	O
alternative	O
methods	O
.	O
</s>
<s>
The	O
Nelder	B-Algorithm
–	I-Algorithm
Mead	I-Algorithm
technique	O
was	O
proposed	O
by	O
John	O
Nelder	O
and	O
Roger	O
Mead	O
in	O
1965	O
,	O
as	O
a	O
development	O
of	O
the	O
method	O
of	O
Spendley	O
et	O
al	O
.	O
</s>
<s>
The	O
method	O
approximates	O
a	O
local	O
optimum	O
of	O
a	O
problem	O
with	O
n	O
variables	O
when	O
the	O
objective	O
function	O
varies	O
smoothly	O
and	O
is	O
unimodal	B-Algorithm
.	O
</s>
<s>
The	O
Nelder	B-Algorithm
–	I-Algorithm
Mead	I-Algorithm
method	I-Algorithm
requires	O
,	O
in	O
the	O
original	O
variant	O
,	O
no	O
more	O
than	O
two	O
evaluations	O
per	O
iteration	O
,	O
except	O
for	O
the	O
shrink	O
operation	O
described	O
later	O
,	O
which	O
is	O
attractive	O
compared	O
to	O
some	O
other	O
direct-search	O
optimization	O
methods	O
.	O
</s>
<s>
Nelder	B-Algorithm
–	I-Algorithm
Mead	I-Algorithm
in	O
n	O
dimensions	O
maintains	O
a	O
set	O
of	O
n+1	O
test	O
points	O
arranged	O
as	O
a	O
simplex	O
.	O
</s>
<s>
The	O
downhill	B-Algorithm
simplex	I-Algorithm
method	I-Algorithm
now	O
takes	O
a	O
series	O
of	O
steps	O
,	O
most	O
steps	O
just	O
moving	O
the	O
point	O
of	O
the	O
simplex	O
where	O
the	O
function	O
is	O
largest	O
(	O
“	O
highest	O
point	O
”	O
)	O
through	O
the	O
opposite	O
face	O
of	O
the	O
simplex	O
to	O
a	O
lower	O
point	O
.	O
</s>
<s>
Unlike	O
modern	O
optimization	O
methods	O
,	O
the	O
Nelder	B-Algorithm
–	I-Algorithm
Mead	I-Algorithm
heuristic	B-Algorithm
can	O
converge	O
to	O
a	O
non-stationary	O
point	O
,	O
unless	O
the	O
problem	O
satisfies	O
stronger	O
conditions	O
than	O
are	O
necessary	O
for	O
modern	O
methods	O
.	O
</s>
<s>
Modern	O
improvements	O
over	O
the	O
Nelder	B-Algorithm
–	I-Algorithm
Mead	I-Algorithm
heuristic	B-Algorithm
have	O
been	O
known	O
since	O
1979	O
.	O
</s>
<s>
A	O
common	O
variant	O
uses	O
a	O
constant-size	O
,	O
small	O
simplex	O
that	O
roughly	O
follows	O
the	O
gradient	O
direction	O
(	O
which	O
gives	O
steepest	B-Algorithm
descent	I-Algorithm
)	O
.	O
</s>
<s>
(	O
This	O
approximates	O
the	O
procedure	O
in	O
the	O
original	O
Nelder	B-Algorithm
–	I-Algorithm
Mead	I-Algorithm
article	O
.	O
)	O
</s>
