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A New Proof Of The Maximum Principle


  • Ngo Van Long
  • Koji Shimomura


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

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    References listed on IDEAS

    1. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586.
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    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 1-8, July.

    More about this item


    Maximum Principle; Envelope Theorem; Principe de Maximum; Théorème de l'Enveloppe;

    JEL classification:

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

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