Optimal control in infinite horizon problems: A Sobolev space approach
AbstractIn this paper, we make use of the Sobolev space W exp.1,1 (R+, R exp.n) to derive at once the Pontryagin conditions for the standard optimal growth model in continuous time, including a necessary and sufficient transversality condition. An application to the Ramsey model is given. We use an order ideal argument to solve the problem inherent to the fact that L exp.1 spaces have natural positive cones with no interior points.
Download InfoIf 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.
Bibliographic InfoPaper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2004089.
Date of creation: 00 Dec 2004
Date of revision:
Contact details of provider:
Postal: Voie du Roman Pays 34, 1348 Louvain-la-Neuve (Belgium)
Fax: +32 10474304
Web page: http://www.uclouvain.be/core
More information through EDIRC
optimal control; Sobolev spaces; transversality conditions; order ideal;
Other versions of this item:
- Cuong Van & Raouf Boucekkine & Cagri Saglam, 2007. "Optimal Control in Infinite Horizon Problems: A Sobolev Space Approach," Economic Theory, Springer, vol. 32(3), pages 497-509, September.
- LE VAN, CUONG & BOUCEKKINE, Raouf & SAGLAM, Cagri, . "Optimal control in infinite horizon problems: A Sobolev space approach," CORE Discussion Papers RP -1956, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Cuong Le Van & Raouf Boucekkine & Cagri Saglam, 2005. "Optimal control in infinite horizon problems : a Sobolev space approach," Cahiers de la Maison des Sciences Economiques b05094, Université Panthéon-Sorbonne (Paris 1).
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
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.:
- Ngo Van Long & Koji Shimomura, 2003. "A Note on Transversality Conditions," Discussion Paper Series 144, Research Institute for Economics & Business Administration, Kobe University.
- Benveniste, L. M. & Scheinkman, J. A., 1982. "Duality theory for dynamic optimization models of economics: The continuous time case," Journal of Economic Theory, Elsevier, vol. 27(1), pages 1-19, June.
- Askenazy, Philippe & Le Van, Cuong, 1999.
"A Model of Optimal Growth Strategy,"
Journal of Economic Theory,
Elsevier, vol. 85(1), pages 24-51, March.
- Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
- Michel, P., 1980.
"On the Transversality Condition in Infinite Horizon Optimal Problems,"
Cahiers de recherche
8024, Universite de Montreal, Departement de sciences economiques.
- Michel, Philippe, 1982. "On the Transversality Condition in Infinite Horizon Optimal Problems," Econometrica, Econometric Society, vol. 50(4), pages 975-85, July.
- Araujo,A. & Monteiro,P.K., 1989. "General equilibrium with infinitely many goods: The case of seperable utilities," Discussion Paper Serie A 249, University of Bonn, Germany.
- Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898 Elsevier.
- Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
- Bonnisseau, Jean-Marc & Le Van, Cuong, 1996. "On the subdifferential of the value function in economic optimization problems," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 55-73.
- Dogan, Erol & Le Van, Cuong & Saglam, Cagri, 2011.
"Optimal timing of regime switching in optimal growth models: A Sobolev space approach,"
Mathematical Social Sciences,
Elsevier, vol. 61(2), pages 97-103, March.
- Cuong Le Van & Erol Dogan & Cagri Saglam, 2011. "Optimal timing of regime switching in optimal growth models: A Sobolev space approach," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00549165, HAL.
- Erol Dogan & Cuong Le Van & Cagri Saglam, 2010. "Optimal timing of regime switching in optimal growth models: A Sobolev space approach," Working Papers 16, Development and Policies Research Center (DEPOCEN), Vietnam.
- Goenka, Aditya & Liu, Lin & Nguyen, Manh-Hung, 2014. "Infectious diseases and economic growth," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 34-53.
- Patrice Pieretti & Skerdilajda Zanaj & Benteng Zou, 2012. "On the long run economic performance of small economies," CREA Discussion Paper Series 12-14, Center for Research in Economic Analysis, University of Luxembourg.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Alain GILLIS).
If references are entirely missing, you can add them using this form.