<s>
MINOS	B-Application
is	O
a	O
Fortran	B-Application
software	O
package	O
for	O
solving	O
linear	O
and	O
nonlinear	O
mathematical	O
optimization	O
problems	O
.	O
</s>
<s>
MINOS	B-Application
(	O
Modular	O
In-core	O
Nonlinear	O
Optimization	O
System	O
)	O
may	O
be	O
used	O
for	O
linear	O
programming	O
,	O
quadratic	O
programming	O
,	O
and	O
more	O
general	O
objective	O
functions	O
and	O
constraints	O
,	O
and	O
for	O
finding	O
a	O
feasible	O
point	O
for	O
a	O
set	O
of	O
linear	O
or	O
nonlinear	O
equalities	O
and	O
inequalities	O
.	O
</s>
<s>
MINOS	B-Application
was	O
first	O
developed	O
by	O
Bruce	O
Murtagh	O
and	O
Michael	O
Saunders	O
,	O
mostly	O
at	O
the	O
Systems	O
Optimization	O
Laboratory	O
in	O
the	O
Department	O
of	O
Operations	O
Research	O
at	O
Stanford	O
University	O
.	O
</s>
<s>
In	O
1985	O
,	O
Saunders	O
was	O
awarded	O
the	O
inaugural	O
Orchard-Hays	O
prize	O
by	O
the	O
Mathematical	O
Programming	O
Society	O
(	O
now	O
the	O
Mathematical	O
Optimization	O
Society	O
)	O
for	O
his	O
work	O
on	O
MINOS	B-Application
.	O
</s>
<s>
MINOS	B-Application
is	O
supported	O
in	O
the	O
AIMMS	B-Application
,	O
AMPL	B-Language
,	O
APMonitor	B-Application
,	O
GAMS	B-Application
,	O
and	O
TOMLAB	B-Application
modeling	O
systems	O
.	O
</s>
<s>
In	O
addition	O
,	O
it	O
remains	O
one	O
of	O
the	O
top-used	O
solvers	O
on	O
the	O
NEOS	O
Server	O
and	O
in	O
GAMS	B-Application
.	O
</s>
<s>
If	O
some	O
or	O
all	O
of	O
the	O
gradients	O
are	O
not	O
provided	O
,	O
MINOS	B-Application
will	O
approximate	O
the	O
missing	O
ones	O
by	O
finite	O
differences	O
,	O
but	O
this	O
could	O
be	O
slow	O
and	O
less	O
reliable	O
.	O
</s>
<s>
For	O
linear	O
programs	O
,	O
a	O
two-phase	O
primal	O
simplex	B-Algorithm
method	I-Algorithm
is	O
used	O
.	O
</s>
<s>
The	O
subproblem	O
objective	O
is	O
an	O
augmented	B-Algorithm
Lagrangian	I-Algorithm
,	O
and	O
the	O
subproblem	O
constraints	O
are	O
linearizations	O
of	O
the	O
nonlinear	O
constraints	O
at	O
the	O
current	O
point	O
.	O
</s>
<s>
MINOS	B-Application
is	O
intended	O
for	O
large	O
sparse	O
problems	O
.	O
</s>
<s>
The	O
source	O
code	O
is	O
suitable	O
for	O
all	O
scientific	O
machines	O
with	O
a	O
Fortran	B-Application
compiler	O
.	O
</s>
