<s>
The	O
GEKKO	B-Application
Python	B-Language
package	O
solves	O
large-scale	O
mixed-integer	O
and	O
differential	O
algebraic	O
equations	O
with	O
nonlinear	B-Algorithm
programming	I-Algorithm
solvers	O
(	O
IPOPT	B-Algorithm
,	O
APOPT	B-Application
,	O
BPOPT	O
,	O
SNOPT	B-Application
,	O
MINOS	O
)	O
.	O
</s>
<s>
In	O
addition	O
,	O
the	O
package	O
solves	O
Linear	B-Algorithm
programming	I-Algorithm
(	O
LP	O
)	O
,	O
Quadratic	B-Algorithm
programming	I-Algorithm
(	O
QP	O
)	O
,	O
Quadratically	O
constrained	O
quadratic	B-Algorithm
program	I-Algorithm
(	O
QCQP	O
)	O
,	O
Nonlinear	B-Algorithm
programming	I-Algorithm
(	O
NLP	O
)	O
,	O
Mixed	O
integer	O
programming	O
(	O
MIP	O
)	O
,	O
and	O
Mixed	O
integer	O
linear	B-Algorithm
programming	I-Algorithm
(	O
MILP	O
)	O
.	O
</s>
<s>
GEKKO	B-Application
is	O
available	O
in	O
Python	B-Language
and	O
installed	O
with	O
pip	O
from	O
PyPI	O
of	O
the	O
Python	B-Language
Software	O
Foundation	O
.	O
</s>
<s>
GEKKO	B-Application
works	O
on	O
all	O
platforms	O
and	O
with	O
Python	B-Language
2.7	O
and	O
3+	O
.	O
</s>
<s>
By	O
default	O
,	O
the	O
problem	O
is	O
sent	O
to	O
a	O
public	O
server	O
where	O
the	O
solution	O
is	O
computed	O
and	O
returned	O
to	O
Python	B-Language
.	O
</s>
<s>
GEKKO	B-Application
is	O
an	O
extension	O
of	O
the	O
APMonitor	B-Application
Optimization	I-Application
Suite	I-Application
but	O
has	O
integrated	O
the	O
modeling	O
and	O
solution	O
visualization	O
directly	O
within	O
Python	B-Language
.	O
</s>
<s>
A	O
mathematical	O
model	O
is	O
expressed	O
in	O
terms	O
of	O
variables	O
and	O
equations	O
such	O
as	O
the	O
Hock	O
&	O
Schittkowski	O
Benchmark	O
Problem	O
#71	O
used	O
to	O
test	O
the	O
performance	O
of	O
nonlinear	B-Algorithm
programming	I-Algorithm
solvers	O
.	O
</s>
<s>
This	O
optimization	O
problem	O
is	O
solved	O
with	O
GEKKO	B-Application
as	O
shown	O
below	O
.	O
</s>
<s>
There	O
are	O
many	O
other	O
references	O
to	O
APMonitor	B-Application
and	O
GEKKO	B-Application
as	O
a	O
sample	O
of	O
the	O
types	O
of	O
applications	O
that	O
can	O
be	O
solved	O
.	O
</s>
<s>
GEKKO	B-Application
is	O
developed	O
from	O
the	O
National	O
Science	O
Foundation	O
(	O
NSF	O
)	O
research	O
grant	O
#1547110	O
and	O
is	O
detailed	O
in	O
a	O
Special	O
Issue	O
collection	O
on	O
combined	O
scheduling	O
and	O
control	O
.	O
</s>
<s>
Other	O
notable	O
mentions	O
of	O
GEKKO	B-Application
are	O
the	O
listing	O
in	O
the	O
Decision	O
Tree	O
for	O
Optimization	O
Software	O
,	O
added	O
support	O
for	O
APOPT	B-Application
and	O
BPOPT	O
solvers	O
,	O
projects	O
reports	O
of	O
the	O
online	O
Dynamic	O
Optimization	O
course	O
from	O
international	O
participants	O
.	O
</s>
<s>
GEKKO	B-Application
is	O
a	O
topic	O
in	O
online	O
forums	O
where	O
users	O
are	O
solving	O
optimization	O
and	O
optimal	O
control	O
problems	O
.	O
</s>
<s>
GEKKO	B-Application
is	O
used	O
for	O
advanced	O
control	O
in	O
the	O
Temperature	O
Control	O
Lab	O
(	O
TCLab	O
)	O
for	O
process	O
control	O
education	O
at	O
20	O
universities	O
.	O
</s>
<s>
In	O
this	O
example	O
,	O
deep	B-Algorithm
learning	I-Algorithm
generates	O
a	O
model	O
from	O
training	O
data	O
that	O
is	O
generated	O
with	O
the	O
function	O
.	O
</s>
<s>
An	O
artificial	B-Architecture
neural	I-Architecture
network	I-Architecture
with	O
three	O
layers	O
is	O
used	O
for	O
this	O
example	O
.	O
</s>
<s>
The	O
program	O
produces	O
parameter	O
weights	O
that	O
minimize	O
the	O
sum	O
of	O
squared	O
errors	O
between	O
the	O
measured	O
data	O
points	O
and	O
the	O
neural	B-Architecture
network	I-Architecture
predictions	O
at	O
those	O
points	O
.	O
</s>
<s>
GEKKO	B-Application
uses	O
gradient-based	O
optimizers	O
to	O
determine	O
the	O
optimal	O
weight	O
values	O
instead	O
of	O
standard	O
methods	O
such	O
as	O
backpropagation	B-Algorithm
.	O
</s>
<s>
The	O
neural	B-Architecture
network	I-Architecture
model	I-Architecture
is	O
tested	O
across	O
the	O
range	O
of	O
training	O
data	O
as	O
well	O
as	O
for	O
extrapolation	O
to	O
demonstrate	O
poor	O
predictions	O
outside	O
of	O
the	O
training	O
data	O
.	O
</s>
<s>
The	O
final	O
part	O
of	O
the	O
script	O
displays	O
the	O
neural	B-Architecture
network	I-Architecture
model	I-Architecture
,	O
the	O
original	O
function	O
,	O
and	O
the	O
sampled	O
data	O
points	O
used	O
for	O
fitting	O
.	O
</s>
<s>
The	O
basic	O
optimal	O
control	O
is	O
solved	O
with	O
GEKKO	B-Application
by	O
integrating	O
the	O
objective	O
and	O
transcribing	O
the	O
differential	O
equation	O
into	O
algebraic	O
form	O
with	O
orthogonal	O
collocation	O
on	O
finite	O
elements	O
.	O
</s>
