IDEAS home Printed from https://ideas.repec.org/p/cir/cirwor/2002s-04.html
   My bibliography  Save this paper

A New Proof Of The Maximum Principle

Author

Listed:
  • Ngo Van Long
  • Koji Shimomura

Abstract

We offer a new proof of the maximum principle for optimal control problems with fixed endpoint. We allow for inequality constraints involving state variables and control variables. Our proof relies on an application of the envelope theorem. Nous donnons une preuve nouvelle du principe de maximum pour les problèmes de contrôle optimal aux points terminaux fixés. Le cas où il y a des contraintes en forme d inégalité est permis. Notre preuve utilise le théorème de l'enveloppe.

Suggested Citation

  • Ngo Van Long & Koji Shimomura, 2002. "A New Proof Of The Maximum Principle," CIRANO Working Papers 2002s-04, CIRANO.
    • Handle: RePEc:cir:cirwor:2002s-04
    as

    Download full text from publisher

    File URL: https://cirano.qc.ca/files/publications/2002s-04.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Caliendo Frank N. & Guo Nick L., 2014. "Optimal Control Problems with State Specific Jumps in the State Equation," Mathematical Economics Letters, De Gruyter, vol. 1(2-4), pages 61-68, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Frédéric Gannon & Vincent Touzé, 2006. "Insurance and Optimal Growth," SciencePo Working papers Main halshs-00085181, HAL.
    2. Alice Issanchou & Karine Daniel & Pierre Dupraz & Carole Ropars-Collet, 2018. "Soil resource and the profitability and sustainability of farms: A soil quality investment model," Working Papers SMART 18-01, INRAE UMR SMART.
    3. Benchekroun, Hassan & van Long, Ngo, 1998. "Efficiency inducing taxation for polluting oligopolists," Journal of Public Economics, Elsevier, vol. 70(2), pages 325-342, November.
    4. Manuel A. Gómez, 2022. "The good, the bad and the worse: current, past and future consumption externalities and equilibrium efficiency," Journal of Economics, Springer, vol. 137(3), pages 195-228, December.
    5. Jason P. Brown & Dayton M. Lambert & Raymond J. G. M. Florax, 2013. "The Birth, Death, and Persistence of Firms: Creative Destruction and the Spatial Distribution of U.S. Manufacturing Establishments, 2000–2006," Economic Geography, Clark University, vol. 89(3), pages 203-226, July.
    6. Laussel, Didier & Resende, Joana, 2014. "Dynamic price competition in aftermarkets with network effects," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 106-118.
    7. Kudła Janusz & Kopczewska Katarzyna & Kocia Agata & Kruszewski Robert & Walczyk Konrad, 2018. "Dynamic Fiscal Solvency with Consumption and Capital Taxes," Central European Economic Journal, Sciendo, vol. 5(52), pages 96-108, January.
    8. Horan, R.D. & Bulte, E.H., 2004. "Optimal and open access harvesting and multi-use species in a second best world," Other publications TiSEM 95000e50-7225-4f4d-aeaf-a, Tilburg University, School of Economics and Management.
    9. Marc GRONWALD & Ngo Van LONG & Luise ROEPKE, 2017. "Three Degrees of Green Paradox: The Weak, The Strong, and the Extreme Green Paradox," Cahiers de recherche 02-2017, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    10. Luigi Siciliani, 2008. "A note on the dynamic interaction between waiting times and waiting lists," Health Economics, John Wiley & Sons, Ltd., vol. 17(5), pages 639-647, May.
    11. Ragni, Stefania & Diele, Fasma & Marangi, Carmela, 2010. "Steady-state invariance in high-order Runge-Kutta discretization of optimal growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(7), pages 1248-1259, July.
    12. Hennessy, David A., 2006. "Feeding and the Equilibrium Feeder Animal Price-Weight Schedule," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 31(2), pages 1-23, August.
    13. Liljas, Bengt, 1998. "The demand for health with uncertainty and insurance," Journal of Health Economics, Elsevier, vol. 17(2), pages 153-170, April.
    14. Wang Ruqu, 2007. "The Optimal Consumption and the Quitting of Harmful Addictive Goods," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 7(1), pages 1-38, February.
    15. Caleiro, António, 2006. "On the Synchronisation of Elections -- A differential Games Approach," EconStor Preprints 142775, ZBW - Leibniz Information Centre for Economics.
    16. Louis-Pascal Mahé & Carole Ropars, 1998. "Régulation de l'exploitation d'une ressource renouvelable : inefficacité d'un rationnement d'input et efficacité des quotas individuels transférables (QIT)," Post-Print hal-02349927, HAL.
    17. Di Falco, Salvatore & Perrings, Charles, 2005. "Crop biodiversity, risk management and the implications of agricultural assistance," Ecological Economics, Elsevier, vol. 55(4), pages 459-466, December.
    18. Silvia Bertarelli & Chiara Lodi & Stefania Ragni, 2022. "An optimal strategy to control mining and recycling of non-renewable resources," Working Papers 2202, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2022.
    19. Brian S. Ferguson, 2000. "Interpreting the rational addiction model," Health Economics, John Wiley & Sons, Ltd., vol. 9(7), pages 587-598, October.
    20. Diele, F. & Marangi, C. & Ragni, S., 2011. "Exponential Lawson integration for nearly Hamiltonian systems arising in optimal control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(5), pages 1057-1067.

    More about this item

    Keywords

    Maximum Principle; Envelope Theorem; Principe de Maximum; Théorème de l'Enveloppe;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cir:cirwor:2002s-04. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Webmaster (email available below). General contact details of provider: https://edirc.repec.org/data/ciranca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.