<s>
In	O
computational	B-General_Concept
engineering	I-General_Concept
,	O
Luus	B-Algorithm
–	I-Algorithm
Jaakola	I-Algorithm
(	O
LJ	O
)	O
denotes	O
a	O
heuristic	B-Algorithm
for	O
global	O
optimization	O
of	O
a	O
real-valued	O
function	O
.	O
</s>
<s>
In	O
engineering	O
use	O
,	O
LJ	O
is	O
not	O
an	O
algorithm	O
that	O
terminates	O
with	O
an	O
optimal	O
solution	O
;	O
nor	O
is	O
it	O
an	O
iterative	B-Algorithm
method	I-Algorithm
that	O
generates	O
a	O
sequence	O
of	O
points	O
that	O
converges	O
to	O
an	O
optimal	O
solution	O
(	O
when	O
one	O
exists	O
)	O
.	O
</s>
<s>
However	O
,	O
when	O
applied	O
to	O
a	O
twice	O
continuously	O
differentiable	O
function	O
,	O
the	O
LJ	O
heuristic	B-Algorithm
is	O
a	O
proper	O
iterative	B-Algorithm
method	I-Algorithm
,	O
that	O
generates	O
a	O
sequence	O
that	O
has	O
a	O
convergent	O
subsequence	O
;	O
for	O
this	O
class	O
of	O
problems	O
,	O
Newton	O
's	O
method	O
is	O
recommended	O
and	O
enjoys	O
a	O
quadratic	O
rate	O
of	O
convergence	O
,	O
while	O
no	O
convergence	O
rate	O
analysis	O
has	O
been	O
given	O
for	O
the	O
LJ	O
heuristic	B-Algorithm
.	O
</s>
<s>
In	O
practice	O
,	O
the	O
LJ	O
heuristic	B-Algorithm
has	O
been	O
recommended	O
for	O
functions	O
that	O
need	O
be	O
neither	O
convex	O
nor	O
differentiable	O
nor	O
locally	O
Lipschitz	O
:	O
The	O
LJ	O
heuristic	B-Algorithm
does	O
not	O
use	O
a	O
gradient	O
or	O
subgradient	O
when	O
one	O
be	O
available	O
,	O
which	O
allows	O
its	O
application	O
to	O
non-differentiable	O
and	O
non-convex	O
problems	O
.	O
</s>
<s>
Luus	O
has	O
applied	O
LJ	O
in	O
optimal	O
control	O
,	O
transformer	B-Algorithm
design	I-Algorithm
,	O
metallurgical	O
processes	O
,	O
and	O
chemical	O
engineering	O
.	O
</s>
<s>
At	O
each	O
step	O
,	O
the	O
LJ	O
heuristic	B-Algorithm
maintains	O
a	O
box	O
from	O
which	O
it	O
samples	O
points	O
randomly	O
,	O
using	O
a	O
uniform	O
distribution	O
on	O
the	O
box	O
.	O
</s>
<s>
The	O
LJ	O
heuristic	B-Algorithm
iterates	O
the	O
following	O
steps	O
:	O
</s>
<s>
Luus	O
notes	O
that	O
ARS	O
(	O
Adaptive	O
Random	B-Algorithm
Search	I-Algorithm
)	O
algorithms	O
proposed	O
to	O
date	O
differ	O
in	O
regard	O
to	O
many	O
aspects	O
.	O
</s>
<s>
Number	O
of	O
internal	O
loops	O
(	O
NIL	O
,	O
the	O
number	O
of	O
random	B-Algorithm
search	I-Algorithm
points	O
in	O
each	O
cycle	O
)	O
.	O
</s>
<s>
For	O
twice	O
continuously	O
differentiable	O
functions	O
,	O
the	O
LJ	O
heuristic	B-Algorithm
generates	O
a	O
sequence	O
of	O
iterates	O
having	O
a	O
convergent	O
subsequence	O
.	O
</s>
<s>
When	O
applied	O
to	O
twice	O
continuously	O
differentiable	O
problems	O
,	O
the	O
LJ	O
heuristic	B-Algorithm
's	O
rate	O
of	O
convergence	O
decreases	O
as	O
the	O
number	O
of	O
dimensions	O
increases	O
.	O
</s>
