<s>
Pattern	B-Algorithm
search	I-Algorithm
(	O
also	O
known	O
as	O
direct	O
search	O
,	O
derivative-free	O
search	O
,	O
or	O
black-box	O
search	O
)	O
is	O
a	O
family	O
of	O
numerical	O
optimization	O
methods	O
that	O
does	O
not	O
require	O
a	O
gradient	O
.	O
</s>
<s>
One	O
such	O
pattern	B-Algorithm
search	I-Algorithm
method	O
is	O
"	O
convergence	O
"	O
(	O
see	O
below	O
)	O
,	O
which	O
is	O
based	O
on	O
the	O
theory	O
of	O
positive	O
bases	O
.	O
</s>
<s>
Optimization	O
attempts	O
to	O
find	O
the	O
best	O
match	O
(	O
the	O
solution	O
that	O
has	O
the	O
lowest	O
error	O
value	O
)	O
in	O
a	O
multidimensional	B-Algorithm
analysis	I-Algorithm
space	O
of	O
possibilities	O
.	O
</s>
<s>
The	O
name	O
"	O
pattern	B-Algorithm
search	I-Algorithm
"	O
was	O
coined	O
by	O
Hooke	O
and	O
Jeeves	O
.	O
</s>
<s>
Convergence	O
is	O
a	O
pattern	B-Algorithm
search	I-Algorithm
method	O
proposed	O
by	O
Yu	O
,	O
who	O
proved	O
that	O
it	O
converges	O
using	O
the	O
theory	O
of	O
positive	O
bases	O
.	O
</s>
<s>
Outside	O
of	O
such	O
classes	O
,	O
pattern	B-Algorithm
search	I-Algorithm
is	O
a	O
heuristic	O
that	O
can	O
provide	O
useful	O
approximate	O
solutions	O
for	O
some	O
issues	O
,	O
but	O
can	O
fail	O
on	O
others	O
.	O
</s>
<s>
Outside	O
of	O
such	O
classes	O
,	O
pattern	B-Algorithm
search	I-Algorithm
is	O
not	O
an	O
iterative	B-Algorithm
method	I-Algorithm
that	O
converges	O
to	O
a	O
solution	O
;	O
indeed	O
,	O
pattern-search	O
methods	O
can	O
converge	O
to	O
non-stationary	O
points	O
on	O
some	O
relatively	O
tame	O
problems	O
.	O
</s>
