IDEAS home Printed from https://ideas.repec.org/h/spr/spochp/978-3-030-89366-8_12.html
   My bibliography  Save this book chapter

Dynamic Optimization

In: Numerical Methods and Optimization

Author

Listed:
  • Jean-Pierre Corriou

    (University of Lorraine)

Abstract

Dynamic optimization deals with problems where the solution depends on time or space. It is exposed under different angles. First, from a purely mathematical point of view, the problem is solved based on variational calculus. First order Euler conditions are demonstrated, and second order Legendre–Clebsch are mentioned. The same problem is discussed using Hamilton–Jacobi framework. Then, dynamic optimization in continuous time is treated in the framework of optimal control. Successively, Euler’s method, Hamilton–Jacobi, and Pontryagin’s maximum principle are exposed. Several detailed examples accompany the different techniques. Numerical issues with different solutions are explained. The continuous-time part is followed by the discrete-time part, i.e. dynamic programming. Bellman’s theory is explained both by backward and forward induction with clear numerical examples.

Suggested Citation

  • Jean-Pierre Corriou, 2021. "Dynamic Optimization," Springer Optimization and Its Applications, in: Numerical Methods and Optimization, chapter 0, pages 653-708, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-89366-8_12
    DOI: 10.1007/978-3-030-89366-8_12
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    References listed on IDEAS

    as
    1. Todorova, Tamara, 2010. "Problems Book to Accompany Mathematics for Economists," MPRA Paper 117866, University Library of Munich, Germany.
    2. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107401396.
    3. Jin Cao & Gerhard Illing, 2019. "Money: Theory and Practice," Springer Texts in Business and Economics, Springer, number 978-3-030-19697-4, April.
    4. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915.
    5. Minner, Stefan, 2003. "Multiple-supplier inventory models in supply chain management: A review," International Journal of Production Economics, Elsevier, vol. 81(1), pages 265-279, January.
    6. Andres Perea, 2010. "Backward Induction versus Forward Induction Reasoning," Games, MDPI, vol. 1(3), pages 1-21, July.
    7. Kennedy, John O. S., 1988. "Principles of dynamic optimization in resource management," Agricultural Economics, Blackwell, vol. 2(1), pages 57-72, June.
    8. Harold Hotelling, 1931. "The Economics of Exhaustible Resources," Journal of Political Economy, University of Chicago Press, vol. 39(2), pages 137-137.
    9. Hagelauer, Patrick & Mora-Camino, Felix, 1998. "A soft dynamic programming approach for on-line aircraft 4D-trajectory optimization," European Journal of Operational Research, Elsevier, vol. 107(1), pages 87-95, May.
    10. Jin Cao & Gerhard Illing, 2019. "Instructor's Manual for Money: Theory and Practice," Springer Texts in Business and Economics, Springer, number 978-3-030-23618-2, April.
    Full references (including those not matched with items on IDEAS)

    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. Perea, Andrés, 2014. "Belief in the opponentsʼ future rationality," Games and Economic Behavior, Elsevier, vol. 83(C), pages 231-254.
    2. Bonanno, Giacomo, 2014. "A doxastic behavioral characterization of generalized backward induction," Games and Economic Behavior, Elsevier, vol. 88(C), pages 221-241.
    3. Giacomo Bonanno, 2021. "Rational play in games: A behavioral approach," Working Papers 344, University of California, Davis, Department of Economics.
    4. Sanjit Dhami & Emma Manifold & Ali al‐Nowaihi, 2021. "Identity and Redistribution: Theory and Evidence," Economica, London School of Economics and Political Science, vol. 88(350), pages 499-531, April.
    5. Pierfrancesco Guarino & Gabriel Ziegler, 2022. "Strategic Behavior under Context Misalignment," Papers 2205.00564, arXiv.org.
    6. Tsakas, Elias, 2014. "Epistemic equivalence of extended belief hierarchies," Games and Economic Behavior, Elsevier, vol. 86(C), pages 126-144.
    7. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2019. "Comprehensive rationalizability," Games and Economic Behavior, Elsevier, vol. 116(C), pages 185-202.
    8. Joseph Y. Halpern & Yoram Moses, 2017. "Characterizing solution concepts in terms of common knowledge of rationality," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 457-473, May.
    9. Lorenzo Bastianello & Mehmet S. Ismail, 2022. "Rationality and correctness in n-player games," Papers 2209.09847, arXiv.org, revised Dec 2023.
    10. Tsakas, E., 2012. "Rational belief hierarchies," Research Memorandum 004, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    11. Shuige Liu, 2018. "Ordered Kripke Model, Permissibility, and Convergence of Probabilistic Kripke Model," Papers 1801.08767, arXiv.org.
    12. Perea, Andrés & Roy, Souvik, 2017. "A new epistemic characterization of ε-proper rationalizability," Games and Economic Behavior, Elsevier, vol. 104(C), pages 309-328.
    13. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    14. Tsakas, E., 2012. "Pairwise mutual knowledge and correlated rationalizability," Research Memorandum 031, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    15. Barelli, Paulo & Galanis, Spyros, 2013. "Admissibility and event-rationality," Games and Economic Behavior, Elsevier, vol. 77(1), pages 21-40.
    16. Shuige Liu, 2019. "Compactification of Extensive Game Structures and Backward Dominance Procedure," Papers 1905.00355, arXiv.org, revised Nov 2020.
    17. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    18. Tsakas, Elias, 2013. "Pairwise epistemic conditions for correlated rationalizability," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 379-384.
    19. Tsakas, Elias, 2014. "Rational belief hierarchies," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 121-127.
    20. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.

    More about this item

    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:spr:spochp:978-3-030-89366-8_12. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.