IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/539.html
   My bibliography  Save this paper

Morse Programs

Author

Listed:
  • Okitsugu Fujiwara

Abstract

Spingarn and Rockafellar [13] showed in a program (Q_{v}^{u}) minimize {f(x) - u^{T}x subject to g(x) = m; that at any local minimum point x of (Q_{v}^{u}) the Jacobian matrix of g at x has full rank, strict complementary slackness holds and the second order sufficiency conditions hold, for almost every matrix{u v} in R^{n} times R^{m} (Lebesgue measure). The purpose of this paper is to explicate the geometry underlying their work and to exploit this geometry in the generic analysis of constrained optimization problems. Namely we show that their work can be reduced to the study of minimizing a Morse function on a manifold with boundary. We follow a classical tradition of first studying an equality constrained program and then reducing inequality constrained programs to a finite family of equality constrained programs, through the device of active (or binding) constraints.

Suggested Citation

  • Okitsugu Fujiwara, 1979. "Morse Programs," Cowles Foundation Discussion Papers 539, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:539
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d05/d0539.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Araujo, Aloisio & Mas-Colell, Andreu, 1978. "Notes on the smoothing of aggregate demand," Journal of Mathematical Economics, Elsevier, vol. 5(2), pages 113-127, September.
    2. Chichilnisky, Graciela & Kalman, Peter J, 1978. "Comparative Statics of Less Neoclassical Agents," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(1), pages 141-148, February.
    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. Chichilnisky, Graciela & Kalman, P.J., 1977. "Properties of critical points and operators in economics," MPRA Paper 7976, University Library of Munich, Germany.
    2. Aureo de Paula, 2004. "Social Interactions in a Synchronization Game," Econometric Society 2004 Latin American Meetings 277, Econometric Society.
    3. Martin Dumav, 2013. "Health Insurance over the Life Cycle with Adverse Selection," 2013 Meeting Papers 1138, Society for Economic Dynamics.
    4. de Paula, Áureo, 2009. "Inference in a synchronization game with social interactions," Journal of Econometrics, Elsevier, vol. 148(1), pages 56-71, January.
    5. Victor Rios-Rull & Dean Corbae: & Satyajit Chatterjee, 2011. "A Theory of Credit Scoring and the Competitive Pricing of Default Risk," 2011 Meeting Papers 1115, Society for Economic Dynamics.
    6. M. Hossein Partovi & Michael R. Caputo, 2006. "A Complete Theory Of Comparative Statics For Differentiable Optimization Problems," Metroeconomica, Wiley Blackwell, vol. 57(1), pages 31-67, February.
    7. Murto, Pauli & Välimäki, Juuso, 2013. "Delay and information aggregation in stopping games with private information," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2404-2435.
    8. José Faro, 2013. "Cobb-Douglas preferences under uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 273-285, October.
    9. F. Desmond Mccarthy, 1981. "Quality Effects in Consumer Behaviour," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 20(2), pages 133-150.
    10. Joël Blot & Bertrand Crettez, 2004. "On the smoothness of optimal paths," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(1), pages 1-34, August.

    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:cwl:cwldpp:539. 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.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.