IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v96y2022i2d10.1007_s00186-022-00789-7.html
   My bibliography  Save this article

The Lagrangian, constraint qualifications and economics

Author

Listed:
  • Sjur D. Flåm

    (University of Bergen)

  • Jan-J. Rückmann

    (University of Bergen)

Abstract

Considering constrained choice, practitioners and theorists frequently invoke a Lagrangian to generate optimality conditions. Regular use of that vehicle requires, however, some constraint qualification. Yet many economists go easy on the mathematics of that issue. Conversely, few mathematicians elaborate on the economics of the context. Thereby both parties leave some lacunas as to didactics or intuition. This note attempts to shed some light on these matters.

Suggested Citation

  • Sjur D. Flåm & Jan-J. Rückmann, 2022. "The Lagrangian, constraint qualifications and economics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(2), pages 215-232, October.
    • Handle: RePEc:spr:mathme:v:96:y:2022:i:2:d:10.1007_s00186-022-00789-7
    DOI: 10.1007/s00186-022-00789-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-022-00789-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00186-022-00789-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    2. LeRoy,Stephen F. & Werner,Jan, 2014. "Principles of Financial Economics," Cambridge Books, Cambridge University Press, number 9781107024120, February.
    3. D.P. Bertsekas & A.E. Ozdaglar, 2002. "Pseudonormality and a Lagrange Multiplier Theory for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 287-343, August.
    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. Shi, Yi & Deng, Yawen & Wang, Guoan & Xu, Jiuping, 2020. "Stackelberg equilibrium-based eco-economic approach for sustainable development of kitchen waste disposal with subsidy policy: A case study from China," Energy, Elsevier, vol. 196(C).
    2. Cheng‐Kuang Wu & Yi‐Ming Chen & Dachrahn Wu & Ching‐Lin Chi, 2020. "A Game Theory Approach for Assessment of Risk and Deployment of Police Patrols in Response to Criminal Activity in San Francisco," Risk Analysis, John Wiley & Sons, vol. 40(3), pages 534-549, March.
    3. Müller, Christoph, 2020. "Robust implementation in weakly perfect Bayesian strategies," Journal of Economic Theory, Elsevier, vol. 189(C).
    4. Hitoshi Matsushima, 2019. "Implementation without expected utility: ex-post verifiability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 575-585, December.
    5. Dasgupta Utteeyo, 2011. "Are Entry Threats Always Credible?," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 11(1), pages 1-41, December.
    6. Baran Han, 2018. "The role and welfare rationale of secondary sanctions: A theory and a case study of the US sanctions targeting Iran," Conflict Management and Peace Science, Peace Science Society (International), vol. 35(5), pages 474-502, September.
    7. Carlos Pimienta & Jianfei Shen, 2014. "On the equivalence between (quasi-)perfect and sequential equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 395-402, May.
    8. Asheim, Geir & Søvik, Ylva, 2003. "The semantics of preference-based belief operators," Memorandum 05/2003, Oslo University, Department of Economics.
    9. Wang, Yafeng & Graham, Brett, 2009. "Generalized Maximum Entropy estimation of discrete sequential move games of perfect information," MPRA Paper 21331, University Library of Munich, Germany.
    10. Karbowski, Adam, 2011. "O kilku modelach samolubnego karania w ekonomii behawioralnej [Evolution of altruism in the light of behavioral economics]," MPRA Paper 69604, University Library of Munich, Germany.
    11. Ricardo F. Reis & Phillip C. Stocken, 2007. "Strategic Consequences of Historical Cost and Fair Value Measurements," Contemporary Accounting Research, John Wiley & Sons, vol. 24(2), pages 557-584, June.
    12. Costello, Christopher & Molina, Renato, 2021. "Transboundary marine protected areas," Resource and Energy Economics, Elsevier, vol. 65(C).
    13. Martin Hellwig & Felix Bierbrauer, 2009. "Public Good Provision in a Large Economy," 2009 Meeting Papers 1062, Society for Economic Dynamics.
    14. Jonathan Hofer, 2024. "Red light game identifies ineffective criminal deterrence," American Journal of Economics and Sociology, Wiley Blackwell, vol. 83(3), pages 673-682, May.
    15. Boyle, Glenn & Irwin, Tim, 2004. "Valuing Managerial Flexibility: A Child's Guide to Real Options," Working Paper Series 3876, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.
    16. Roberto Andreani & José Mario Martínez & Alberto Ramos & Paulo J. S. Silva, 2018. "Strict Constraint Qualifications and Sequential Optimality Conditions for Constrained Optimization," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 693-717, August.
    17. Ünsal Özdilek, 2020. "Land and building separation based on Shapley values," Palgrave Communications, Palgrave Macmillan, vol. 6(1), pages 1-13, December.
    18. Arantza Estévez-Fernández & Peter Borm & M. Gloria Fiestras-Janeiro, 2020. "Nontransferable utility bankruptcy games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 154-177, April.
    19. Sjur Didrik Flåm, 2013. "Reaching Market Equilibrium Merely by Bilateral Barters," CESifo Working Paper Series 4504, CESifo.
    20. Asheim, G.B. & Dufwenberg, M., 1996. "Admissibility and Common Knowledge," Discussion Paper 1996-16, Tilburg University, Center for Economic Research.

    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:mathme:v:96:y:2022:i:2:d:10.1007_s00186-022-00789-7. 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.