<s>
AMPL	B-Language
(	O
A	O
Mathematical	O
Programming	O
Language	O
)	O
is	O
an	O
algebraic	B-Application
modeling	I-Application
language	I-Application
to	O
describe	O
and	O
solve	O
high-complexity	O
problems	O
for	O
large-scale	O
mathematical	O
computing	O
(	O
i.e.	O
,	O
large-scale	O
optimization	O
and	O
scheduling-type	O
problems	O
)	O
.	O
</s>
<s>
AMPL	B-Language
supports	O
dozens	O
of	O
solvers	B-Application
,	O
both	O
open	B-Application
source	I-Application
and	O
commercial	B-Application
software	I-Application
,	O
including	O
CBC	O
,	O
CPLEX	B-Application
,	O
FortMP	B-Application
,	O
MINOS	B-Application
,	O
IPOPT	B-Algorithm
,	O
SNOPT	B-Application
,	O
KNITRO	B-Application
,	O
and	O
LGO	O
.	O
</s>
<s>
Problems	O
are	O
passed	O
to	O
solvers	B-Application
as	O
nl	B-Application
files	O
.	O
</s>
<s>
AMPL	B-Language
is	O
used	O
by	O
more	O
than	O
100	O
corporate	O
clients	O
,	O
and	O
by	O
government	O
agencies	O
and	O
academic	O
institutions	O
.	O
</s>
<s>
One	O
advantage	O
of	O
AMPL	B-Language
is	O
the	O
similarity	O
of	O
its	O
syntax	O
to	O
the	O
mathematical	O
notation	O
of	O
optimization	O
problems	O
.	O
</s>
<s>
Many	O
modern	O
solvers	B-Application
available	O
on	O
the	O
NEOS	B-Application
Server	I-Application
(	O
formerly	O
hosted	O
at	O
the	O
Argonne	O
National	O
Laboratory	O
,	O
currently	O
hosted	O
at	O
the	O
University	O
of	O
Wisconsin	O
,	O
Madison	O
)	O
accept	O
AMPL	B-Language
input	O
.	O
</s>
<s>
According	O
to	O
the	O
NEOS	O
statistics	O
AMPL	B-Language
is	O
the	O
most	O
popular	O
format	O
for	O
representing	O
mathematical	O
programming	O
problems	O
.	O
</s>
<s>
AMPL	B-Language
features	O
a	O
mix	O
of	O
declarative	B-Language
and	O
imperative	B-Application
programming	I-Application
styles	O
.	O
</s>
<s>
Formulating	O
optimization	O
models	O
occurs	O
via	O
declarative	B-Language
language	I-Language
elements	O
such	O
as	O
sets	O
,	O
scalar	O
and	O
multidimensional	O
parameters	O
,	O
decision	O
variables	O
,	O
objectives	O
and	O
constraints	B-Application
,	O
which	O
allow	O
for	O
concise	O
description	O
of	O
most	O
problems	O
in	O
the	O
domain	O
of	O
mathematical	O
optimization	O
.	O
</s>
<s>
the	O
construction	O
of	O
hybrid	O
algorithms	O
for	O
problem	O
types	O
for	O
which	O
no	O
direct	O
efficient	O
solvers	B-Application
are	O
available	O
.	O
</s>
<s>
To	O
support	O
re-use	O
and	O
simplify	O
construction	O
of	O
large-scale	O
optimization	O
problems	O
,	O
AMPL	B-Language
allows	O
separation	O
of	O
model	O
and	O
data	O
.	O
</s>
<s>
AMPL	B-Language
supports	O
a	O
wide	O
range	O
of	O
problem	O
types	O
,	O
among	O
them	O
:	O
</s>
<s>
AMPL	B-Language
invokes	O
a	O
solver	B-Application
in	O
a	O
separate	O
process	O
which	O
has	O
these	O
advantages	O
:	O
</s>
<s>
Interaction	O
with	O
the	O
solver	B-Application
is	O
done	O
through	O
a	O
well-defined	O
nl	B-Application
interface	I-Application
.	O
</s>
<s>
AMPL	B-Language
is	O
available	O
for	O
many	O
popular	O
32	O
-	O
and	O
64-bit	O
operating	B-General_Concept
systems	I-General_Concept
including	O
Linux	B-Application
,	O
macOS	B-Application
,	O
Solaris	B-Application
,	O
AIX	B-Application
,	O
and	O
Windows	B-Application
.	O
</s>
<s>
The	O
translator	O
is	O
proprietary	B-Application
software	I-Application
maintained	O
by	O
AMPL	B-Language
Optimization	O
LLC	O
.	O
</s>
<s>
However	O
,	O
several	O
online	O
services	O
exist	O
,	O
providing	O
free	O
modeling	O
and	O
solving	O
facilities	O
using	O
AMPL	B-Language
.	O
</s>
<s>
AMPL	B-Language
can	O
be	O
used	O
from	O
within	O
Microsoft	B-Application
Excel	I-Application
via	O
the	O
SolverStudio	B-Operating_System
Excel	B-Application
add-in	O
.	O
</s>
<s>
The	O
AMPL	B-Language
Solver	B-Application
Library	O
(	O
ASL	O
)	O
,	O
which	O
allows	O
reading	O
nl	B-Application
files	O
and	O
provides	O
the	O
automatic	B-Algorithm
differentiation	I-Algorithm
,	O
is	O
open-source	B-Application
.	O
</s>
<s>
It	O
is	O
used	O
in	O
many	O
solvers	B-Application
to	O
implement	O
AMPL	B-Language
connection	O
.	O
</s>
<s>
This	O
table	O
present	O
significant	O
steps	O
in	O
AMPL	B-Language
history	O
.	O
</s>
<s>
Year	O
Highlights	O
1985	O
AMPL	B-Language
was	O
designed	O
and	O
implemented	O
1990	O
Paper	O
describing	O
the	O
AMPL	B-Language
modeling	O
language	O
was	O
published	O
in	O
Management	O
Science	O
1991	O
AMPL	B-Language
supports	O
nonlinear	B-Algorithm
programming	I-Algorithm
and	O
automatic	B-Algorithm
differentiation	I-Algorithm
1993	O
Robert	O
Fourer	O
,	O
David	O
Gay	O
and	O
Brian	O
Kernighan	O
were	O
awarded	O
ORSA/CSTS	O
Prize	O
by	O
the	O
Operations	O
Research	O
Society	O
of	O
America	O
,	O
for	O
writings	O
on	O
the	O
design	O
of	O
mathematical	O
programming	O
systems	O
and	O
the	O
AMPL	B-Language
modeling	O
language	O
1995	O
Extensions	O
for	O
representing	O
piecewise-linear	O
and	O
network	O
structures	O
1995	O
Scripting	O
constructs	O
1997	O
Enhanced	O
support	O
for	O
nonlinear	O
solvers	B-Application
1998	O
AMPL	B-Language
supports	O
complementarity	O
theory	O
problems	O
2000	O
Relational	O
database	O
and	O
spreadsheet	B-Application
access	O
2002	O
Support	O
for	O
constraint	B-Application
programming	I-Application
2003	O
AMPL	B-Language
Optimization	O
LLC	O
was	O
founded	O
by	O
the	O
inventors	O
of	O
AMPL	B-Language
,	O
Robert	O
Fourer	O
,	O
David	O
Gay	O
,	O
and	O
Brian	O
Kernighan	O
.	O
</s>
<s>
The	O
new	O
company	O
took	O
over	O
the	O
development	O
and	O
support	O
of	O
the	O
AMPL	B-Language
modeling	O
language	O
from	O
Lucent	O
Technologies	O
,	O
Inc	O
.	O
2005	O
AMPL	B-Language
Modeling	O
Language	O
Google	O
group	O
opened	O
2008	O
Kestrel	O
:	O
An	O
AMPL	B-Language
Interface	O
to	O
the	O
NEOS	B-Application
Server	I-Application
introduced	O
2012	O
Robert	O
Fourer	O
,	O
David	O
Gay	O
,	O
and	O
Brian	O
Kernighan	O
were	O
awarded	O
the	O
2012	O
INFORMS	O
Impact	O
Prize	O
as	O
the	O
originators	O
of	O
one	O
of	O
the	O
most	O
important	O
algebraic	B-Application
modeling	I-Application
languages	I-Application
.	O
</s>
<s>
A	O
transportation	O
problem	O
from	O
George	O
Dantzig	O
is	O
used	O
to	O
provide	O
a	O
sample	O
AMPL	B-Language
model	O
.	O
</s>
<s>
Here	O
is	O
a	O
partial	O
list	O
of	O
solvers	B-Application
supported	O
by	O
AMPL	B-Language
:	O
</s>
<s>
Solver	B-Application
Supported	O
problem	O
types	O
APOPT	B-Application
mixed	O
integer	O
nonlinear	B-Algorithm
programming	I-Algorithm
Artelys	B-Application
Knitro	I-Application
linear	B-Algorithm
,	O
quadratic	O
and	O
nonlinear	B-Algorithm
programming	I-Algorithm
Bonmin	O
mixed	O
integer	O
nonlinear	B-Algorithm
programming	I-Algorithm
BPMPD	O
linear	B-Algorithm
and	O
quadratic	B-Algorithm
programming	I-Algorithm
COIN-OR	B-Application
CBC	O
mixed	O
integer	O
programming	O
COIN-OR	B-Application
CLP	O
linear	B-Algorithm
programming	I-Algorithm
CONOPT	O
nonlinear	B-Algorithm
programming	I-Algorithm
Couenne	B-Application
mixed	O
integer	O
nonlinear	B-Algorithm
programming	I-Algorithm
(	O
MINLP	O
)	O
CPLEX	B-Application
linear	B-Algorithm
,	O
quadratic	O
,	O
second-order	B-Algorithm
cone	I-Algorithm
and	O
mixed	O
integer	O
programming	O
CPLEX	B-Application
CP	O
Optimizer	O
constraint	B-Application
programming	I-Application
FILTER	O
nonlinear	B-Algorithm
programming	I-Algorithm
FortMP	B-Application
linear	B-Algorithm
,	O
quadratic	O
and	O
mixed	O
integer	O
programming	O
Gecode	B-Application
constraint	B-Application
programming	I-Application
IPOPT	B-Algorithm
nonlinear	B-Algorithm
programming	I-Algorithm
JaCoP	B-Application
constraint	B-Application
programming	I-Application
LGO	O
global	O
and	O
local	O
nonlinear	B-Algorithm
optimization	I-Algorithm
lp_solve	O
linear	B-Algorithm
and	O
mixed	O
integer	O
programming	O
MINOS	B-Application
linear	B-Algorithm
and	O
nonlinear	B-Algorithm
programming	I-Algorithm
MINTO	B-Application
mixed	O
integer	O
programming	O
MOSEK	B-Application
linear	B-Algorithm
,	O
mixed	O
integer	O
linear	B-Algorithm
,	O
quadratic	O
,	O
mixed	O
integer	O
quadratic	O
,	O
quadratically	O
constrained	O
,	O
conic	O
and	O
convex	O
nonlinear	B-Algorithm
programming	I-Algorithm
Octeract	B-Application
Engine	I-Application
All	O
types	O
of	O
optimisation	O
problems	O
without	O
differential	O
or	O
integral	O
terms	O
,	O
including	O
discontinuous	O
problems	O
with	O
and	O
elementary	O
functions	O
.	O
</s>
