View source for Isomerization of Alpha-Pinene problem

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-->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])



== 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_2) y_1, \\
 & \dot{y}_2 & = & \theta_1 y_1,  \\
 & \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}_5 & = & \theta_4 y_3 - \theta_5 y_5.  \\
\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 [[Isomerization of Alpha-Pinene problem (TACO)]]


<!--List of all categories this page is part of. List characterization of solution behavior, model properties, ore presence of implementation details (e.g., AMPL for AMPL model) here -->
[[Category:MIOCP]]
[[Category:ODE model]]