Marine population dynamics problem

Marine population dynamics problem
State dimension:	1
Differential states:	n_2

The Marine population dynamics problem estimates growth and mortality rates of a marine species at each stage (for example ages or development stage) given the population as a function of time.( Problem taken from the COPS library)

Mathematical formulation

The problem is given by

$\begin{array}{llcl} \min_{g_{j}, m_{j}} & \sum_{j = 1}^{n_{m}} & | | y (τ_{j}; m, g) - z_{j} | |^{2} \\ s.t. & {\dot{y}}_{j} & = & g_{j - 1} y_{j - 1} - (m_{j} + g_{j}) y_{j} \forall j \in 1, . . ., n_{s}, \\ g_{j}, m_{j} & \in & [0, 1] . \end{array}$

where $g_{j}$ and $m_{j}$ are the growth and mortality rates at stage $j$ respectively and the initial conditions are unknown. The error between computed and observed data is minimized.

Parameters

There are $n_{s}$ stages and $n_{m}$ timepoints at which the error is minimized.

Source Code

Model descriptions are available in

AMPL/TACO code at Marine population dynamics problem (TACO)