Numerical computation of the optimal vector field: Exemplified by a fishery model
Numerous optimal control models analyzed in economics are formulated as discounted infinite time horizon problems, where the defining functions are nonlinear as well in the states as in the controls. As a consequence solutions can often only be found numerically. Moreover, the long run optimal solutions are mostly limit sets like equilibria or limit cycles. Using these specific solutions a BVP approach together with a continuation technique is used to calculate the parameter dependent dynamic structure of the optimal vector field. We use a one dimensional optimal control model of a fishery to exemplify the numerical techniques. But these methods are applicable to a much wider class of optimal control problems with a moderate number of state and control variables.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
- Peter Kunkel & Oskar von dem Hagen, 2000. "Numerical Solution of Infinite-Horizon Optimal-Control Problems," Computational Economics, Society for Computational Economics, vol. 16(3), pages 189-205, December.
- Michel, Philippe, 1982.
"On the Transversality Condition in Infinite Horizon Optimal Problems,"
Econometric Society, vol. 50(4), pages 975-85, July.
- Michel, P., 1980. "On the Transversality Condition in Infinite Horizon Optimal Problems," Cahiers de recherche 8024, Universite de Montreal, Departement de sciences economiques.
- Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-72, March.
- Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Hartl, Richard F. & Kort, Peter M., 2011. "Two state capital accumulation with heterogenous products: Disruptive vs. non-disruptive goods," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 462-478, April.
- Levy, Amnon & Neri, Frank, 2004.
"Macroeconomic Aspects of Substance Abuse: Diffusion, Productivity and Optimal Control,"
Economics Working Papers
wp04-22, School of Economics, University of Wollongong, NSW, Australia.
- Levy, Amnon & Neri, Frank & Grass, Dieter, 2006. "Macroeconomic Aspects Of Substance Abuse: Diffusion, Productivity And Optimal Control," Macroeconomic Dynamics, Cambridge University Press, vol. 10(02), pages 145-164, April.
- Hartl, Richard F., 1987. "A simple proof of the monotonicity of the state trajectories in autonomous control problems," Journal of Economic Theory, Elsevier, vol. 41(1), pages 211-215, February.
- Anne-Sophie Crépin, 2007. "Using Fast and Slow Processes to Manage Resources with Thresholds," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 36(2), pages 191-213, February.
- Kiseleva, T. & Wagener, F.O.O., 2011. "Bifurcations of Optimal Vector Fields," CeNDEF Working Papers 11-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- Jonathan P. Caulkins & Gustav Feichtinger & Dieter Grass & Michael Johnson & Gernot Tragler & Yuri Yegorov, 2005. "Placing the poor while keeping the rich in their place," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 13(1), pages 1-34, July.
When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:36:y:2012:i:10:p:1626-1658. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.