<s>
The	O
TomSym	B-Application
MATLAB	B-Language
symbolic	O
modeling	B-Application
engine	O
is	O
a	O
platform	O
for	O
modeling	B-Application
applied	O
optimization	O
and	O
optimal	O
control	O
problems	O
.	O
</s>
<s>
TomSym	B-Application
is	O
complete	O
modeling	B-Application
environment	O
in	O
Matlab	B-Language
with	O
support	O
for	O
most	O
built-in	O
mathematical	O
operators	O
in	O
Matlab	B-Language
.	O
</s>
<s>
It	O
is	O
a	O
combined	O
modeling	B-Application
,	O
compilation	B-Application
and	O
interface	O
to	O
the	O
TOMLAB	B-Application
solvers	O
.	O
</s>
<s>
The	O
matrix	B-Architecture
derivative	I-Architecture
of	O
a	O
matrix	O
function	O
is	O
a	O
fourth	O
rank	O
tensor	B-Device
-	O
that	O
is	O
,	O
a	O
matrix	O
each	O
of	O
whose	O
entries	O
is	O
a	O
matrix	O
.	O
</s>
<s>
Rather	O
than	O
using	O
four-dimensional	O
matrices	O
to	O
represent	O
this	O
,	O
TomSym	B-Application
continues	O
to	O
work	O
in	O
two	O
dimensions	O
.	O
</s>
<s>
This	O
makes	O
it	O
possible	O
to	O
take	O
advantage	O
of	O
the	O
very	O
efficient	O
handling	O
of	O
sparse	B-Algorithm
matrices	I-Algorithm
in	O
Matlab	B-Language
,	O
which	O
is	O
not	O
available	O
for	O
higher-dimensional	O
matrices	O
.	O
</s>
<s>
TomSym	B-Application
has	O
a	O
variety	O
of	O
functions	O
,	O
among	O
them	O
:	O
</s>
<s>
Ability	O
to	O
transform	O
expressions	O
and	O
generate	O
analytical	O
first	O
and	O
second	O
order	O
derivatives	B-Algorithm
,	O
including	O
sparsity	B-Algorithm
patterns	O
.	O
</s>
<s>
Interfaced	O
and	O
compatible	O
with	O
MAD	B-Algorithm
,	O
i.e.	O
</s>
<s>
MAD	B-Algorithm
can	O
be	O
used	O
when	O
symbolic	O
modeling	B-Application
is	O
not	O
suitable	O
.	O
</s>
<s>
Ability	O
to	O
analyze	O
p-coded	B-Language
Matlab	B-Language
files	O
.	O
</s>
<s>
The	O
TomSym	B-Application
symbolic	O
source	O
transformation	O
makes	O
it	O
possible	O
to	O
define	O
any	O
the	O
set	O
of	O
decision	O
variables	O
(	O
both	O
continuous	O
and	O
integer	O
)	O
and	O
any	O
type	O
of	O
constraint	O
as	O
well	O
as	O
scalars	O
and	O
constant	O
parameters	O
.	O
</s>
<s>
An	O
example	O
linear	B-Algorithm
programming	I-Algorithm
problem	I-Algorithm
would	O
look	O
like	O
this	O
:	O
</s>
<s>
A	O
MINLP	O
problem	O
is	O
defined	O
just	O
like	O
a	O
linear	B-Algorithm
programming	I-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
This	O
example	O
also	O
shows	O
how	O
to	O
convert	O
the	O
model	O
into	O
a	O
general	O
TOMLAB	B-Application
problem	O
.	O
</s>
<s>
tomSym	B-Application
makes	O
it	O
possible	O
to	O
build	O
models	O
with	O
two	O
or	O
more	O
variable	O
indices	O
in	O
MATLAB	B-Language
.	O
</s>
<s>
For	O
functions	O
that	O
cannot	O
be	O
interpreted	O
by	O
tomSym	B-Application
it	O
is	O
possible	O
to	O
use	O
either	O
automatic	B-Algorithm
differentiation	I-Algorithm
or	O
numerical	O
differentiation	O
.	O
</s>
