# Methanol to Hydrocarbons problem

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Methanol to Hydrocarbons problem
Algebraic states: 3
Continuous control values: 5
Path constraints: 5

The Methanol to Hydrocarbons problem tries to determine "reaction coefficients for the conversion of methanol into various hydrocarbons." (Cite and problem taken from the COPS library)

## Mathematical formulation

The problem is given by

$\begin{array}{llcl} \displaystyle \min_{\theta} &\sum\limits_{j=1}^{16} &&||y(\tau_j; \theta) - z_j||^2 \\[1.5ex] \mbox{s.t.} & \dot{y}_1 & = & -( 2 \theta_2 - \frac{\theta_1 y_2}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 + \theta_4) y_1, \\[0.3cm] & \dot{y}_2 & = & \frac{\theta_1 y_1 (\theta_2 y_1 - y_2)}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 y_1, \\[0.3cm] & \dot{y}_3 & = & \frac{\theta_1 y_1 (y_2 + \theta_5 y_1}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_4 y_1, \\[0.3cm] & \theta_i & \geq & 0 \quad i = 1,...,5. \end{array}$

## Parameters

The values $z_j$ are measurements for the concentration for $y$ at time points $\tau_1, ..., \tau_{16}$ and initial conditions are known.

## Source Code

Model descriptions are available in