IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v171y2016i3d10.1007_s10957-015-0795-8.html
   My bibliography  Save this article

(Convex) Level Sets Integration

Author

Listed:
  • Jean-Pierre Crouzeix

    (Université Blaise Pascal)

  • Andrew Eberhard

    (RMIT University)

  • Daniel Ralph

    (University of Cambridge)

Abstract

The paper addresses the problem of recovering a pseudoconvex function from the normal cones to its level sets that we call the convex level sets integration problem. An important application is the revealed preference problem. Our main result can be described as integrating a maximally cyclically pseudoconvex multivalued map that sends vectors or “bundles” of a Euclidean space to convex sets in that space. That is, we are seeking a pseudoconvex (real) function such that the normal cone at each boundary point of each of its lower level sets contains the set value of the multivalued map at the same point. This raises the question of uniqueness of that function up to rescaling. Even after normalizing the function long an orienting direction, we give a counterexample to its uniqueness. We are, however, able to show uniqueness under a condition motivated by the classical theory of ordinary differential equations.

Suggested Citation

  • Jean-Pierre Crouzeix & Andrew Eberhard & Daniel Ralph, 2016. "(Convex) Level Sets Integration," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 865-886, December.
  • Handle: RePEc:spr:joptap:v:171:y:2016:i:3:d:10.1007_s10957-015-0795-8
    DOI: 10.1007/s10957-015-0795-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-015-0795-8
    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/s10957-015-0795-8?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. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    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. Jean-Pierre Crouzeix, 2022. "On Quasiconvex Functions Which are Convexifiable or Not," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 66-80, June.
    2. Suliman Al-Homidan & Nicolas Hadjisavvas & Loai Shaalan, 2018. "Transformation of Quasiconvex Functions to Eliminate Local Minima," Journal of Optimization Theory and Applications, Springer, vol. 177(1), pages 93-105, April.

    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. Brocas, Isabelle & Carrillo, Juan D. & Combs, T. Dalton & Kodaverdian, Niree, 2019. "The development of consistent decision-making across economic domains," Games and Economic Behavior, Elsevier, vol. 116(C), pages 217-240.
    2. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
    3. Stephen L. Cheung & Agnieszka Tymula & Xueting Wang, 2022. "Present bias for monetary and dietary rewards," Experimental Economics, Springer;Economic Science Association, vol. 25(4), pages 1202-1233, September.
    4. Ian Crawford, 2004. "Necessary and sufficient conditions for latent separability," CeMMAP working papers CWP02/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. James L Swofford, 2000. "Microeconomic foundations of an optimal currency area," Review of Financial Economics, John Wiley & Sons, vol. 9(2), pages 121-128, December.
    6. Laura Blow & Martin Browning & Ian Crawford, 2004. "Nonparametric methods for the characteristic model," CeMMAP working papers 18/04, Institute for Fiscal Studies.
    7. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2018. "Transitivity of preferences: when does it matter?," Theoretical Economics, Econometric Society, vol. 13(3), September.
    8. Richard Blundell & Martin Browning & Laurens Cherchye & Ian Crawford & Bram De Rock & Frederic Vermeulen, 2012. "Sharp for SARP: Nonparametric bounds on the behavioural and welfare effects of price changes," IFS Working Papers W12/14, Institute for Fiscal Studies.
    9. Pawel Dziewulski, 2016. "Eliciting the just-noticeable difference," Economics Series Working Papers 798, University of Oxford, Department of Economics.
    10. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc0o6ctj2 is not listed on IDEAS
    11. Cherchye, Laurens & Chiappori, Pierre-André & De Rock, Bram & Ringdal, Charlotte & Vermeulen, Frederic, 2021. "Feed the Children," IZA Discussion Papers 14687, Institute of Labor Economics (IZA).
    12. Thomas Demuynck, 2014. "The computational complexity of rationalizing Pareto optimal choice behavior," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 529-549, March.
    13. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    14. Anne Épaulard & Jean-Pierre Laffargue & Pierre Malgrange, 2008. "Présentation générale," Economie & Prévision, La Documentation Française, vol. 0(2), pages 1-13.
    15. Pamela Jakiela, 2013. "Equity vs. efficiency vs. self-interest: on the use of dictator games to measure distributional preferences," Experimental Economics, Springer;Economic Science Association, vol. 16(2), pages 208-221, June.
    16. Laurens Cherchye & Bram De Rock & Rachel Griffith & Martin O'Connell & Kate Smith & Frederic Vermeulen, 2017. "A New Year, a New You ?Heterogeneity and Self-control in Food Purchases," Working Papers ECARES ECARES 2017-46, ULB -- Universite Libre de Bruxelles.
    17. Deb, Rahul, 2009. "A testable model of consumption with externalities," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1804-1816, July.
    18. James Andreoni, 2006. "Giving Gifts to Groups: How Congestible is Altruism?," Levine's Bibliography 321307000000000166, UCLA Department of Economics.
    19. David Ahn & Syngjoo Choi & Douglas Gale & Shachar Kariv, 2014. "Estimating ambiguity aversion in a portfolio choice experiment," Quantitative Economics, Econometric Society, vol. 5, pages 195-223, July.
    20. Andreas C Drichoutis & Rodolfo M Nayga, 2020. "Economic Rationality under Cognitive Load," The Economic Journal, Royal Economic Society, vol. 130(632), pages 2382-2409.

    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:joptap:v:171:y:2016:i:3:d:10.1007_s10957-015-0795-8. 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.