<s>
Derivative-free	B-Algorithm
optimization	I-Algorithm
(	O
sometimes	O
referred	O
to	O
as	O
blackbox	O
optimization	O
)	O
,	O
is	O
a	O
discipline	O
in	O
mathematical	O
optimization	O
that	O
does	O
not	O
use	O
derivative	B-Algorithm
information	O
in	O
the	O
classical	O
sense	O
to	O
find	O
optimal	O
solutions	O
:	O
Sometimes	O
information	O
about	O
the	O
derivative	B-Algorithm
of	O
the	O
objective	O
function	O
f	O
is	O
unavailable	O
,	O
unreliable	O
or	O
impractical	O
to	O
obtain	O
.	O
</s>
<s>
For	O
example	O
,	O
f	O
might	O
be	O
non-smooth	O
,	O
or	O
time-consuming	O
to	O
evaluate	O
,	O
or	O
in	O
some	O
way	O
noisy	O
,	O
so	O
that	O
methods	O
that	O
rely	O
on	O
derivatives	B-Algorithm
or	O
approximate	O
them	O
via	O
finite	B-Algorithm
differences	I-Algorithm
are	O
of	O
little	O
use	O
.	O
</s>
<s>
The	O
problem	O
to	O
find	O
optimal	O
points	O
in	O
such	O
situations	O
is	O
referred	O
to	O
as	O
derivative-free	B-Algorithm
optimization	I-Algorithm
,	O
algorithms	O
that	O
do	O
not	O
use	O
derivatives	B-Algorithm
or	O
finite	B-Algorithm
differences	I-Algorithm
are	O
called	O
derivative-free	O
algorithms	O
.	O
</s>
<s>
Derivative-based	O
algorithms	O
use	O
derivative	B-Algorithm
information	O
of	O
to	O
find	O
a	O
good	O
search	O
direction	O
,	O
since	O
for	O
example	O
the	O
gradient	O
gives	O
the	O
direction	O
of	O
steepest	O
ascent	O
.	O
</s>
<s>
Derivative-based	O
optimization	O
is	O
efficient	O
at	O
finding	O
local	O
optima	O
for	O
continuous-domain	O
smooth	O
single-modal	O
problems	O
.	O
</s>
<s>
is	O
disconnected	O
,	O
or	O
(	O
mixed	O
-	O
)	O
integer	O
,	O
or	O
when	O
is	O
expensive	O
to	O
evaluate	O
,	O
or	O
is	O
non-smooth	O
,	O
or	O
noisy	O
,	O
so	O
that	O
(	O
numeric	O
approximations	O
of	O
)	O
derivatives	B-Algorithm
do	O
not	O
provide	O
useful	O
information	O
.	O
</s>
<s>
A	O
slightly	O
different	O
problem	O
is	O
when	O
is	O
multi-modal	O
,	O
in	O
which	O
case	O
local	O
derivative-based	O
methods	O
only	O
give	O
local	O
optima	O
,	O
but	O
might	O
miss	O
the	O
global	O
one	O
.	O
</s>
<s>
In	O
derivative-free	B-Algorithm
optimization	I-Algorithm
,	O
various	O
methods	O
are	O
employed	O
to	O
address	O
these	O
challenges	O
using	O
only	O
function	O
values	O
of	O
,	O
but	O
no	O
derivatives	B-Algorithm
.	O
</s>
<s>
Notable	O
derivative-free	B-Algorithm
optimization	I-Algorithm
algorithms	O
include	O
:	O
</s>
