<s>
Artelys	B-Application
Knitro	I-Application
is	O
a	O
commercial	B-Application
software	I-Application
package	O
for	O
solving	O
large	O
scale	O
nonlinear	O
mathematical	O
optimization	O
problems	O
.	O
</s>
<s>
KNITRO	B-Application
–	O
(	O
the	O
original	O
solver	O
name	O
)	O
short	O
for	O
"	O
Nonlinear	O
Interior	B-Algorithm
point	I-Algorithm
Trust	O
Region	O
Optimization	O
"	O
(	O
the	O
"	O
K	O
"	O
is	O
silent	O
)	O
–	O
was	O
co-created	O
by	O
Richard	O
Waltz	O
,	O
Jorge	O
Nocedal	O
,	O
Todd	O
Plantenga	O
and	O
Richard	O
Byrd	O
.	O
</s>
<s>
Optimization	O
problems	O
must	O
be	O
presented	O
to	O
Knitro	B-Application
in	O
mathematical	O
form	O
,	O
and	O
should	O
provide	O
a	O
way	O
of	O
computing	O
function	O
derivatives	O
using	O
sparse	B-Algorithm
matrices	I-Algorithm
(	O
Knitro	B-Application
can	O
compute	O
derivatives	O
approximation	O
but	O
in	O
most	O
cases	O
providing	O
the	O
exact	O
derivatives	O
is	O
beneficial	O
)	O
.	O
</s>
<s>
An	O
often	O
easier	O
approach	O
is	O
to	O
develop	O
the	O
optimization	O
problem	O
in	O
an	O
algebraic	B-Application
modeling	I-Application
language	I-Application
.	O
</s>
<s>
The	O
modeling	O
environment	O
computes	O
function	O
derivatives	O
,	O
and	O
Knitro	B-Application
is	O
called	O
as	O
a	O
"	O
solver	O
"	O
from	O
within	O
the	O
environment	O
.	O
</s>
<s>
Knitro	B-Application
is	O
specialized	O
for	O
nonlinear	B-Algorithm
optimization	I-Algorithm
but	O
also	O
solves	O
a	O
wide	O
range	O
of	O
optimization	O
problems	O
:	O
</s>
<s>
Artelys	B-Application
Knitro	I-Application
contains	O
a	O
wide	O
range	O
of	O
optimization	O
algorithms	O
.	O
</s>
<s>
Knitro	B-Application
offers	O
four	O
different	O
optimization	O
algorithms	O
for	O
solving	O
optimization	O
problems	O
.	O
</s>
<s>
Two	O
algorithms	O
are	O
of	O
the	O
interior	B-Algorithm
point	I-Algorithm
type	O
,	O
and	O
two	O
are	O
of	O
the	O
active	B-Algorithm
set	I-Algorithm
type	O
.	O
</s>
<s>
These	O
algorithms	O
are	O
known	O
to	O
have	O
fundamentally	O
different	O
characteristics	O
;	O
for	O
example	O
,	O
interior	B-Algorithm
point	I-Algorithm
methods	I-Algorithm
follow	O
a	O
path	O
through	O
the	O
interior	O
of	O
the	O
feasible	O
region	O
while	O
active	B-Algorithm
set	I-Algorithm
methods	I-Algorithm
tend	O
to	O
stay	O
at	O
the	O
boundaries	O
.	O
</s>
<s>
Knitro	B-Application
provides	O
both	O
types	O
of	O
algorithm	O
for	O
greater	O
flexibility	O
in	O
solving	O
problems	O
,	O
and	O
allows	O
crossover	O
during	O
the	O
solution	O
process	O
from	O
one	O
algorithm	O
to	O
another	O
.	O
</s>
<s>
Knitro	B-Application
provides	O
tools	O
for	O
solving	O
optimization	O
models	O
(	O
both	O
linear	O
and	O
nonlinear	O
)	O
with	O
binary	O
or	O
integer	O
variables	O
.	O
</s>
<s>
The	O
Knitro	B-Application
mixed	O
integer	O
programming	O
(	O
MIP	O
)	O
code	O
offers	O
three	O
algorithms	O
for	O
mixed-integer	O
nonlinear	B-Algorithm
programming	I-Algorithm
(	O
MINLP	O
)	O
:	O
</s>
<s>
Artelys	B-Application
Knitro	I-Application
supports	O
a	O
variety	O
of	O
programming	O
and	O
modeling	O
languages	O
including	O
.	O
</s>
<s>
Artelys	B-Application
Knitro	I-Application
also	O
includes	O
a	O
number	O
of	O
key	O
features	O
:	O
</s>
<s>
Artelys	B-Application
Knitro	I-Application
is	O
available	O
on	O
the	O
following	O
platforms	O
:	O
</s>
