<s>
Random	B-Algorithm
optimization	I-Algorithm
(	O
RO	O
)	O
is	O
a	O
family	O
of	O
numerical	O
optimization	O
methods	O
that	O
do	O
not	O
require	O
the	O
gradient	O
of	O
the	O
problem	O
to	O
be	O
optimized	O
and	O
RO	O
can	O
hence	O
be	O
used	O
on	O
functions	O
that	O
are	O
not	O
continuous	O
or	O
differentiable	O
.	O
</s>
<s>
The	O
name	O
random	B-Algorithm
optimization	I-Algorithm
is	O
attributed	O
to	O
Matyas	O
who	O
made	O
an	O
early	O
presentation	O
of	O
RO	O
along	O
with	O
basic	O
mathematical	O
analysis	O
.	O
</s>
<s>
This	O
algorithm	O
corresponds	O
to	O
a	O
(	O
1+1	O
)	O
evolution	B-Algorithm
strategy	I-Algorithm
with	O
constant	O
step-size	O
.	O
</s>
<s>
Matyas	O
showed	O
the	O
basic	O
form	O
of	O
RO	O
converges	B-Algorithm
to	O
the	O
optimum	O
of	O
a	O
simple	O
unimodal	O
function	O
by	O
using	O
a	O
limit-proof	B-Algorithm
which	O
shows	O
convergence	B-Algorithm
to	O
the	O
optimum	O
is	O
certain	O
to	O
occur	O
if	O
a	O
potentially	O
infinite	O
number	O
of	O
iterations	O
are	O
performed	O
.	O
</s>
<s>
In	O
fact	O
,	O
such	O
a	O
theoretical	O
limit-proof	B-Algorithm
will	O
also	O
show	O
that	O
purely	O
random	O
sampling	O
of	O
the	O
search-space	O
will	O
inevitably	O
yield	O
a	O
sample	O
arbitrarily	O
close	O
to	O
the	O
optimum	O
.	O
</s>
<s>
Mathematical	O
analyses	O
are	O
also	O
conducted	O
by	O
Baba	O
and	O
Solis	O
and	O
Wets	O
to	O
establish	O
that	O
convergence	B-Algorithm
to	O
a	O
region	O
surrounding	O
the	O
optimum	O
is	O
inevitable	O
under	O
some	O
mild	O
conditions	O
for	O
RO	O
variants	O
using	O
other	O
probability	O
distributions	O
for	O
the	O
sampling	O
.	O
</s>
