Simple Examples
Apps.SimpleExamples History
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{$\begin{align}\mathrm{minimize} \quad & 100-x_1^2-2x_2^2-x_3^2-x_1x_2-x_1x_3 \\ \mathrm{subject\;to}\quad & 8x_1+14x_2+7x_3=56 \\ & x_1^2+x_2^2+x_3^2\geq0 \\ & x_1,x_2,x_3\ge0 \end{align}$}
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{$\begin{align}\mathrm{minimize} \quad & 100-x_1^2-2x_2^2-x_3^2-x_1x_2-x_1x_3 \\ \mathrm{subject\;to}\quad & 8x_1+14x_2+7x_3=56 \\ & x_1^2+x_2^2+x_3^2\geq25 \\ & x_1,x_2,x_3\ge0 \end{align}$}
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* %list list-page% [[Attach:min2.apm | View APMonitor min2.apm]]
'''Solve with [[https://gekko.readthedocs.io/en/latest/|Python Gekko]]'''
(:source lang=python:)
(:source lang=python:)
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* %list list-page% [[Attach:min2.apm | View APMonitor Solution]]
* Solve with [[https://gekko.readthedocs.io/en/latest/|Python Gekko]]
-> (:source lang=python:)
* Solve with [[https://gekko.readthedocs.io/en/latest/|Python Gekko]]
-> (:source lang=python:)
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* %list list-page% [[Attach:min2.apm | View APMonitor min2.apm]]
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{$\begin{align}\mathrm{minimize} \quad & 100-x_1^2-2x_2^2-x_3^2-x_1x_2-x_1x_3 \\ \mathrm{subject\;to}\quad & 8x_1+14x_2+7x_3=56 \\ & x_1^2+x_2^2+x_3^2\geq0 \\ & x_1,x_2,x_3\ge0 \end{align}$}
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'''Solve with'' [[https://gekko.readthedocs.io/en/latest/|Python Gekko]]'''
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'''Solve with [[https://gekko.readthedocs.io/en/latest/|Python Gekko]]'''
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'''Solve with'' [[https://gekko.readthedocs.io/en/latest/|Python Gekko]]'''
(:source lang=python:)
from gekko import GEKKO
m = GEKKO(remote=False)
x1,x2,x3 = m.Array(m.Var,3,lb=0)
m.Minimize(1000-x1**2-2*x2**2-x3**2-x1*x2-x1*x3)
m.Equations([8*x1+14*x2+7*x3==56,
x1**2+x2**2+x3**2>=25])
m.solve(disp=False)
print(x1.value,x2.value,x3.value)
(:sourceend:)
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!! Simple Examples
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!! Tutorial Examples
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!! Simple test problem with 2 local minima
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!!!! Test problem with 2 local minima
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!!!! Numerical Integration
This problem demonstrates how to numerically integrate a function. In this case, the function of interest is ''x = 2 t'' with an exact solution of ''y = t'^2^' ''.
Attach:integration_model.png
The following Python script runs the model and plots the results:
Attach:integration_script.png
Attach:integration_results.png
[[Attach:integration_script.zip | Download integration example problem]]
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Models presented below are a test suite of optimization problems. They are part of the test suite used to verify modifications to the %blue%A%red%P%black%Monitor software. Users may also find this collection useful to compare %blue%A%red%P%black%Monitor syntax to other modeling languages, for solver benchmarking, or as example problems in optimization. Models may be submitted through the %blue%[[https://apmonitor.ath.cx/sandbox/ | online submission platform]].
to:
Models presented below are a test suite of optimization problems. They are part of the test suite used to verify modifications to the %blue%A%red%P%black%Monitor software. Users may also find this collection useful to compare %blue%A%red%P%black%Monitor syntax to other modeling languages, for solver benchmarking, or as example problems in optimization. Models may be submitted through the (:html:)<a href="/online/view_pass.php">Online Web-based Interface</a>(:htmlend:).
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This optimization problem has 2 local minima. The two problem solutions are found at (0,0,8) with objective 936.0 (global minimum) and (7,0,0) with objective 951.0.
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!! Simple Examples
Models presented below are a test suite of optimization problems. They are part of the test suite used to verify modifications to the %blue%A%red%P%black%Monitor software. Users may also find this collection useful to compare %blue%A%red%P%black%Monitor syntax to other modeling languages, for solver benchmarking, or as example problems in optimization. Models may be submitted through the %blue%[[https://apmonitor.ath.cx/sandbox/ | online submission platform]].
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!! Simple test problem with 2 local minima
* %list list-page% [[Attach:min2.apm | View min2.apm]]
Attach:min2.png
----
!! Hock & Schittkowski Collection
* Link to [[HockSchittkowski | Hock & Schittkowski Collection]] page
* %list list-page% [[Attach:hs.zip | All 119 models in the collection (hs.zip)]]
----
Models presented below are a test suite of optimization problems. They are part of the test suite used to verify modifications to the %blue%A%red%P%black%Monitor software. Users may also find this collection useful to compare %blue%A%red%P%black%Monitor syntax to other modeling languages, for solver benchmarking, or as example problems in optimization. Models may be submitted through the %blue%[[https://apmonitor.ath.cx/sandbox/ | online submission platform]].
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!! Simple test problem with 2 local minima
* %list list-page% [[Attach:min2.apm | View min2.apm]]
Attach:min2.png
----
!! Hock & Schittkowski Collection
* Link to [[HockSchittkowski | Hock & Schittkowski Collection]] page
* %list list-page% [[Attach:hs.zip | All 119 models in the collection (hs.zip)]]
----