View source for Methanol to Hydrocarbons problem

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|nz        = 3
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-->The Methanol to Hydrocarbons problem tries to determine "reaction coefficients for the conversion of methanol into various hydrocarbons." (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}^{16} &&||y(\tau_j; \theta) - z_j||^2   \\[1.5ex]
 \mbox{s.t.} 
 & \dot{y}_1 & = &  -( 2 \theta_2 - \frac{\theta_1 y_2}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 + \theta_4) y_1, \\[0.3cm]
 & \dot{y}_2 & = & \frac{\theta_1 y_1 (\theta_2 y_1 - y_2)}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 y_1,  \\[0.3cm]
 & \dot{y}_3 & = & \frac{\theta_1 y_1 (y_2 + \theta_5 y_1}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_4 y_1,  \\[0.3cm]
 & \theta_i & \geq & 0 \quad i = 1,...,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_{16} </math> and initial conditions are known.

== Source Code ==

Model descriptions are available in

* [[:Category:AMPL/TACO | AMPL/TACO code]] at [[Methanol to Hydrocarbons 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]]
[[Category:Chemical engineering]]