Marine population dynamics problem - Revision history

FelixMueller at 08:31, 27 July 2016

2016-07-27T08:31:49Z

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	\|nz = <math> n_s </math>		\|nz = <math> n_s </math>
	\|np = <math> 2 n_s </math>		\|np = <math> 2 n_s </math>
			\|nc = <math> 4 n_s </math>
	}}<!-- 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: /* Mathematical formulation */

2016-07-04T09:54:22Z

Mathematical formulation

← Older revision		Revision as of 09:54, 4 July 2016
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	<math>		<math>
	\begin{array}{llcl}		\begin{array}{llcl}
	\displaystyle \min_{g, m} & \sum\limits_{j=1}^{~~n_m~~} &&\|\|y(\tau_j; g, m) - z_j\|\|^2 \\[1.5ex]		\displaystyle \min_{g, m} & \sum\limits_{j=1}^{n_s} &&\|\|y(\tau_j; g, m) - z_j\|\|^2 \\[1.5ex]
	\mbox{s.t.}		\mbox{s.t.}
	& \dot{y}_j & = & g_{j-1} y_{j-1} - (m_j + g_j) y_j \qquad \forall j \in 1, ..., n_s,\\		& \dot{y}_j & = & g_{j-1} y_{j-1} - (m_j + g_j) y_j \qquad \forall j \in 1, ..., n_s,\\

FelixMueller at 22:11, 27 June 2016

2016-06-27T22:11:24Z

← Older revision		Revision as of 22:11, 27 June 2016
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	[[Category:MIOCP]]		[[Category:MIOCP]]
	[[Category:ODE model]]		[[Category:ODE model]]
			[[Category:Population dynamics]]

FelixMueller at 18:02, 5 May 2016

2016-05-05T18:02:09Z

← Older revision		Revision as of 18:02, 5 May 2016
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	{{Dimensions		{{Dimensions
	\|nz = n_s		\|nz = <math> n_s </math>
	\|np = 2 n_s		\|np = <math> 2 n_s </math>
	}}<!-- 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 18:01, 5 May 2016

2016-05-05T18:01:50Z

← Older revision		Revision as of 18:01, 5 May 2016
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	{{Dimensions		{{Dimensions
	\|nd = 1		\|nz = n_s
	\|nx = ~~n_2~~		\|np = 2 n_s
	}}<!-- 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: /* Mathematical formulation */

2016-05-05T17:59:59Z

Mathematical formulation

← Older revision		Revision as of 17:59, 5 May 2016
Line 15:		Line 15:
	<math>		<math>
	\begin{array}{llcl}		\begin{array}{llcl}
	\displaystyle \min_{~~g_j~~, ~~m_j~~} & \sum\limits_{j=1}^{n_m} &&\|\|y(\tau_j; m~~, g~~) - z_j\|\|^2 \\[1.5ex]		\displaystyle \min_{g, m} & \sum\limits_{j=1}^{n_m} &&\|\|y(\tau_j; g, m) - z_j\|\|^2 \\[1.5ex]
	\mbox{s.t.}		\mbox{s.t.}
	& \dot{y}_j & = & g_{j-1} y_{j-1} - (m_j + g_j) y_j \~~quad~~ \forall j \in 1, ..., n_s,\\		& \dot{y}_j & = & g_{j-1} y_{j-1} - (m_j + g_j) y_j \qquad \forall j \in 1, ..., n_s,\\
	& g_j, m_j &\in& [0,1].		& g_j, m_j &\in& [0,1].
	\end{array}		\end{array}

FelixMueller: Created page with "{{Dimensions |nd = 1 |nx = n_2 }}The Marine population dynamics problem estima..."

2016-05-05T17:59:29Z

Created page with "{{Dimensions |nd = 1 |nx = n_2 }}The Marine population dynamics problem estima..."

New page

{{Dimensions
|nd = 1
|nx = 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 [http://www.mcs.anl.gov/~more/cops/ COPS library])

== Mathematical formulation ==

The problem is given by

<p>
<math>
\begin{array}{llcl}
\displaystyle \min_{g_j, m_j} & \sum\limits_{j=1}^{n_m} &&||y(\tau_j; m, g) - z_j||^2 \\[1.5ex]
\mbox{s.t.}
& \dot{y}_j & = & g_{j-1} y_{j-1} - (m_j + g_j) y_j \quad \forall j \in 1, ..., n_s,\\
& g_j, m_j &\in& [0,1].
\end{array}
</math>
</p>

where <math> g_j </math> and <math> m_j </math> are the growth and mortality rates at stage <math> j </math> respectively and the initial conditions are unknown.
The error between computed and observed data is minimized.

== Parameters ==
There are <math> n_s </math> stages and <math> n_m </math> timepoints at which the error is minimized.

== Source Code ==

Model descriptions are available in

* [[:Category:AMPL/TACO | AMPL/TACO code]] at [[Marine population dynamics problem (TACO)]]


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