<s>
IPOPT	B-Algorithm
,	O
short	O
for	O
"	O
Interior	O
Point	O
OPTimizer	O
,	O
pronounced	O
I-P-Opt	O
"	O
,	O
is	O
a	O
software	B-Library
library	I-Library
for	O
large	O
scale	O
nonlinear	B-Algorithm
optimization	I-Algorithm
of	O
continuous	O
systems	O
.	O
</s>
<s>
It	O
is	O
written	O
in	O
Fortran	B-Application
and	O
C	B-Language
and	O
is	O
released	O
under	O
the	O
EPL	B-License
(	O
formerly	O
CPL	O
)	O
.	O
</s>
<s>
IPOPT	B-Algorithm
implements	O
a	O
primal-dual	O
interior	B-Algorithm
point	I-Algorithm
method	I-Algorithm
,	O
and	O
uses	O
line	O
searches	O
based	O
on	O
Filter	O
methods	O
(	O
Fletcher	O
and	O
Leyffer	O
)	O
.	O
</s>
<s>
IPOPT	B-Algorithm
can	O
be	O
called	O
from	O
various	O
modeling	O
environments	O
and	O
C	B-Language
.	O
</s>
<s>
IPOPT	B-Algorithm
is	O
part	O
of	O
the	O
COIN-OR	B-Application
project	O
.	O
</s>
<s>
IPOPT	B-Algorithm
is	O
designed	O
to	O
exploit	O
1st	O
and	O
2nd	O
derivative	O
(	O
Hessians	O
)	O
information	O
if	O
provided	O
(	O
usually	O
via	O
automatic	B-Algorithm
differentiation	I-Algorithm
routines	O
in	O
modeling	O
environments	O
such	O
as	O
AMPL	B-Language
)	O
.	O
</s>
<s>
If	O
no	O
Hessians	O
are	O
provided	O
,	O
IPOPT	B-Algorithm
will	O
approximate	O
them	O
using	O
a	O
quasi-Newton	B-Algorithm
methods	I-Algorithm
,	O
specifically	O
a	O
BFGS	B-Algorithm
update	I-Algorithm
.	O
</s>
<s>
IPOPT	B-Algorithm
was	O
originally	O
developed	O
by	O
Ph.D.	O
student	O
and	O
Prof	O
.	O
of	O
the	O
Department	O
of	O
Chemical	O
Engineering	O
at	O
Carnegie	O
Mellon	O
University	O
.	O
</s>
<s>
Arvind	O
Raghunathan	O
later	O
created	O
an	O
extension	O
to	O
IPOPT	B-Algorithm
for	O
Mathematical	O
programming	O
with	O
equilibrium	O
constraints	O
(	O
MPEC	O
)	O
.	O
</s>
<s>
This	O
version	O
of	O
IPOPT	B-Algorithm
is	O
generally	O
known	O
as	O
IPOPT-C	O
(	O
with	O
the	O
'	O
C	B-Language
 '	O
standing	O
for	O
'	O
complementarity	O
 '	O
)	O
.	O
</s>
<s>
While	O
in	O
theory	O
any	O
mixed-integer	O
program	O
can	O
be	O
recast	O
as	O
an	O
MPEC	O
,	O
it	O
may	O
or	O
may	O
not	O
be	O
solvable	O
with	O
IPOPT-C	O
.	O
</s>
<s>
Solution	O
of	O
MINLPs	O
(	O
Mixed-Integer	O
Nonlinear	O
Programs	O
)	O
using	O
IPOPT	B-Algorithm
is	O
still	O
being	O
explored	O
.	O
</s>
<s>
and	O
Andreas	O
Wächter	O
are	O
the	O
developers	O
of	O
IPOPT	B-Algorithm
3.0	O
,	O
which	O
is	O
a	O
re-implementation	O
of	O
IPOPT	B-Algorithm
in	O
C++	B-Language
.	O
</s>
