Isomerization of Alpha-Pinene problem - Revision history

FelixMueller at 19:22, 29 September 2016

2016-09-29T19:22:33Z

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FelixMueller at 08:32, 27 July 2016

2016-07-27T08:32:36Z

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	& \dot{y}_4 & = & \theta_3 y_3, \\		& \dot{y}_4 & = & \theta_3 y_3, \\
	& \dot{y}_5 & = & \theta_4 y_3 - \theta_5 y_5, \\		& \dot{y}_5 & = & \theta_4 y_3 - \theta_5 y_5, \\
	& \theta_i & \geq & 0.		& \theta_i & \geq & 0 \quad i = 1,...,5.
	\end{array}		\end{array}
	</math>		</math>

FelixMueller at 08:30, 27 July 2016

2016-07-27T08:30:15Z

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	\|nz = 5		\|nz = 5
	\|np = 5		\|np = 5
			\|nc = 5
	}}<!-- Do not insert line break here or Dimensions Box moves up in the layout...		}}<!-- Do not insert line break here or Dimensions Box moves up in the layout...

FelixMueller at 22:10, 27 June 2016

2016-06-27T22:10:31Z

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FelixMueller: /* Mathematical formulation */

2016-05-05T18:09:18Z

Mathematical formulation

← Older revision		Revision as of 18:09, 5 May 2016
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	& \dot{y}_3 & = & \theta_2 y_1 - (\theta_3 + \theta_4) y_3 + \theta_5 y_5, \\		& \dot{y}_3 & = & \theta_2 y_1 - (\theta_3 + \theta_4) y_3 + \theta_5 y_5, \\
	& \dot{y}_4 & = & \theta_3 y_3, \\		& \dot{y}_4 & = & \theta_3 y_3, \\
	& \dot{y}_5 & = & \theta_4 y_3 - \theta_5 y_5. \\		& \dot{y}_5 & = & \theta_4 y_3 - \theta_5 y_5, \\
			& \theta_i & \geq & 0.
	\end{array}		\end{array}
	</math>		</math>

FelixMueller at 17:48, 5 May 2016

2016-05-05T17:48:40Z

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	-->The Isomerization of Alpha-Pinene problem tries to determine "reaction ~~coe�cients~~ in the thermal isometrization of <math> \alpha </math>-Pinene." (Cite and problem taken from the [http://www.mcs.anl.gov/~more/cops/ COPS library])		-->The Isomerization of Alpha-Pinene problem tries to determine "reaction coefficients in the thermal isometrization of <math> \alpha </math>-Pinene." (Cite and problem taken from the [http://www.mcs.anl.gov/~more/cops/ COPS library])


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	\displaystyle \min_{\theta} &\sum\limits_{j=1}^{8} &&\|\|y(\tau_j; \theta) - z_j\|\|^2 \\[1.5ex]		\displaystyle \min_{\theta} &\sum\limits_{j=1}^{8} &&\|\|y(\tau_j; \theta) - z_j\|\|^2 \\[1.5ex]
	\mbox{s.t.}		\mbox{s.t.}
	& \dot{y}_1 & = & -(\theta_1 + \~~theta_3~~) y_1^2, \\		& \dot{y}_1 & = & -(\theta_1 + \theta_2) y_1, \\
	& \dot{y}_2 & = & \theta_1 y_1~~^2 - \theta_2 y_2.~~ \\		& \dot{y}_2 & = & \theta_1 y_1, \\
	& \dot{y}_3 & = & \~~theta_1~~ y_1^2 - \~~theta_2 y_2.~~ \\		& \dot{y}_3 & = & \theta_2 y_1 - (\theta_3 + \theta_4) y_3 + \theta_5 y_5, \\
	& \dot{y}_4 & = & \~~theta_1 y_1^2 - \theta_2 y_2.~~ \\		& \dot{y}_4 & = & \theta_3 y_3, \\
	& \dot{y}_5 & = & \~~theta_1 y_1^2~~ - \~~theta_2 y_2~~. \\		& \dot{y}_5 & = & \theta_4 y_3 - \theta_5 y_5. \\
	\end{array}		\end{array}
	</math>		</math>
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	Model descriptions are available in		Model descriptions are available in

	* [[:Category:AMPL/TACO \| AMPL/TACO code]] at [[~~Catalytic cracking~~ problem (TACO)]]		* [[:Category:AMPL/TACO \| AMPL/TACO code]] at [[Isomerization of Alpha-Pinene problem (TACO)]]

FelixMueller: Created page with "{{Dimensions |nz = 5 |np = 5 }}The Isomerization of Alpha-Pinene problem tries..."

2016-05-05T17:47:02Z

Created page with "{{Dimensions |nz = 5 |np = 5 }}The Isomerization of Alpha-Pinene problem tries..."

New page

{{Dimensions
|nz = 5
|np = 5
}}The Isomerization of Alpha-Pinene problem tries to determine "reaction coe�cients in the thermal isometrization of <math> \alpha </math>-Pinene." (Cite and problem taken from the [http://www.mcs.anl.gov/~more/cops/ COPS library])

== Mathematical formulation ==

The problem is given by

<p>
<math>
\begin{array}{llcl}
\displaystyle \min_{\theta} &\sum\limits_{j=1}^{8} &&||y(\tau_j; \theta) - z_j||^2 \\[1.5ex]
\mbox{s.t.}
& \dot{y}_1 & = & -(\theta_1 + \theta_3) y_1^2, \\
& \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2. \\
& \dot{y}_3 & = & \theta_1 y_1^2 - \theta_2 y_2. \\
& \dot{y}_4 & = & \theta_1 y_1^2 - \theta_2 y_2. \\
& \dot{y}_5 & = & \theta_1 y_1^2 - \theta_2 y_2. \\
\end{array}
</math>
</p>

== Parameters ==
The values <math> z_j </math> are measurements for the concentration for <math> y </math> at time points <math> \tau_1, ..., \tau_8 </math> and initial conditions are known.

== Source Code ==

Model descriptions are available in

* [[:Category:AMPL/TACO | AMPL/TACO code]] at [[Catalytic cracking problem (TACO)]]


[[Category:MIOCP]]
[[Category:ODE model]]