<s>
The	O
general	B-Application
algebraic	I-Application
modeling	I-Application
system	I-Application
(	O
GAMS	O
)	O
is	O
a	O
high-level	O
modeling	B-Application
system	O
for	O
mathematical	O
optimization	O
.	O
</s>
<s>
GAMS	O
is	O
designed	O
for	O
modeling	B-Application
and	O
solving	O
linear	B-Algorithm
,	O
nonlinear	B-Algorithm
,	O
and	O
mixed-integer	O
optimization	O
problems	O
.	O
</s>
<s>
The	O
system	O
is	O
tailored	O
for	O
complex	O
,	O
large-scale	O
modeling	B-Application
applications	O
and	O
allows	O
the	O
user	O
to	O
build	O
large	O
maintainable	O
models	O
that	O
can	O
be	O
adapted	O
to	O
new	O
situations	O
.	O
</s>
<s>
Models	O
are	O
portable	B-Architecture
from	O
one	O
platform	O
to	O
another	O
.	O
</s>
<s>
GAMS	O
was	O
the	O
first	O
algebraic	B-Application
modeling	I-Application
language	I-Application
(	O
AML	O
)	O
and	O
is	O
formally	O
similar	O
to	O
commonly	O
used	O
fourth-generation	B-Language
programming	I-Language
languages	I-Language
.	O
</s>
<s>
GAMS	O
contains	O
an	O
integrated	B-Application
development	I-Application
environment	I-Application
(	O
IDE	O
)	O
and	O
is	O
connected	O
to	O
a	O
group	O
of	O
third-party	O
optimization	O
solvers	B-Application
.	O
</s>
<s>
Among	O
these	O
solvers	B-Application
are	O
BARON	B-Application
,	O
COIN-OR	B-Application
solvers	B-Application
,	O
CONOPT	O
,	O
CPLEX	B-Application
,	O
DICOPT	O
,	O
MOSEK	B-Application
,	O
SNOPT	B-Application
,	O
SULUM	O
,	O
and	O
XPRESS	B-Application
.	O
</s>
<s>
GAMS	O
allows	O
the	O
users	O
to	O
implement	O
a	O
sort	O
of	O
hybrid	B-Algorithm
algorithm	I-Algorithm
combining	O
different	O
solvers	B-Application
.	O
</s>
<s>
GAMS	O
is	O
among	O
the	O
most	O
popular	O
input	O
formats	O
for	O
the	O
NEOS	B-Application
Server	I-Application
.	O
</s>
<s>
1978	O
Phase	O
I	O
:	O
GAMS	O
supports	O
linear	B-Algorithm
programming	I-Algorithm
.	O
</s>
<s>
1979	O
Phase	O
II	O
:	O
GAMS	O
supports	O
nonlinear	B-Algorithm
programming	I-Algorithm
.	O
</s>
<s>
The	O
prize	O
was	O
awarded	O
to	O
the	O
originators	O
of	O
the	O
five	O
most	O
important	O
algebraic	B-Application
modeling	I-Application
languages	I-Application
.	O
</s>
<s>
GAMS	O
’s	O
impetus	O
for	O
development	O
arose	O
from	O
the	O
frustrating	O
experience	O
of	O
a	O
large	O
economic	O
modeling	B-Application
group	O
at	O
the	O
World	O
Bank	O
.	O
</s>
<s>
Their	O
models	O
just	O
could	O
not	O
be	O
moved	O
to	O
other	O
environments	O
,	O
because	O
special	O
programming	O
knowledge	O
was	O
needed	O
,	O
and	O
data	O
formats	O
and	O
solution	O
methods	O
were	O
not	O
portable	B-Architecture
.	O
</s>
<s>
Using	O
generator	O
matrices	O
for	O
linear	B-Algorithm
programs	I-Algorithm
revealed	O
the	O
importance	O
of	O
naming	O
rows	O
and	O
columns	O
in	O
a	O
consistent	O
manner	O
.	O
</s>
<s>
Experience	O
using	O
traditional	O
programming	O
languages	O
to	O
manage	O
those	O
name	O
spaces	O
naturally	O
lead	O
one	O
to	O
think	O
in	O
terms	O
of	O
sets	O
and	O
tuples	B-Application
,	O
and	O
this	O
led	O
to	O
the	O
relational	O
data	O
model	O
.	O
</s>
<s>
However	O
,	O
translating	O
this	O
rigorous	O
mathematical	O
representation	O
into	O
the	O
algorithm-specific	O
format	O
required	O
the	O
computation	O
of	O
partial	O
derivatives	B-Algorithm
on	O
very	O
large	O
systems	O
.	O
</s>
<s>
In	O
the	O
1970s	O
,	O
TRW	O
developed	O
a	O
system	O
called	O
PROSE	B-Application
that	O
took	O
the	O
ideas	O
of	O
chemical	O
engineers	O
to	O
compute	O
point	O
derivatives	B-Algorithm
that	O
were	O
exact	O
derivatives	B-Algorithm
at	O
a	O
given	O
point	O
,	O
and	O
to	O
embed	O
them	O
in	O
a	O
consistent	O
,	O
Fortran-style	O
calculus	O
modeling	B-Language
language	I-Language
.	O
</s>
<s>
The	O
resulting	O
system	O
allowed	O
the	O
user	O
to	O
use	O
automatically	O
generated	O
exact	O
first	O
and	O
second	O
order	O
derivatives	B-Algorithm
.	O
</s>
<s>
However	O
,	O
PROSE	B-Application
had	O
a	O
number	O
of	O
shortcomings	O
:	O
it	O
could	O
not	O
handle	O
large	O
systems	O
,	O
problem	O
representation	O
was	O
tied	O
to	O
an	O
array-type	O
data	O
structure	O
that	O
required	O
address	O
calculations	O
,	O
and	O
the	O
system	O
did	O
not	O
provide	O
access	O
to	O
state-of-the	O
art	O
solution	O
methods	O
.	O
</s>
<s>
From	O
linear	B-Algorithm
programming	I-Algorithm
,	O
GAMS	O
learned	O
that	O
exploitation	O
of	O
sparsity	O
was	O
key	O
to	O
solving	O
large	O
problems	O
.	O
</s>
<s>
In	O
Linear	B-Algorithm
Programming	I-Algorithm
and	O
Extensions	O
.	O
</s>
<s>
The	O
Mathematical	O
Programming	O
System	O
for	O
General	O
Equilibrium	O
analysis	O
(	O
MPSGE	B-Application
)	O
is	O
a	O
language	O
used	O
for	O
formulating	O
and	O
solving	O
Arrow	O
–	O
Debreu	O
economic	O
equilibrium	O
models	O
and	O
exists	O
as	O
a	O
subsystem	O
within	O
GAMS	O
.	O
</s>
