IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v105y2001i1p109-15310.1023-a1013353515966.html
   My bibliography  Save this article

The Fundamental Relations between Geometric Programming Duality, Parametric Programming Duality, and Ordinary Lagrangian Duality

Author

Listed:
  • Elmor Peterson

Abstract

Every formulation of mathematical programming duality (known to the author) for continuous finite-dimensional optimization can easily be viewed as a special case of at least one of the following three formulations: the geometric programming formulation (of the generalized geometric programming type), the parametric programming formulation (of the generalized Rockafellar-perturbation type), and the ordinary Lagrangian formulation (of the generalized Falk type). The relative strengths and weaknesses of these three duality formulations are described herein, as are the fundamental relations between them. As a theoretical application, the basic duality between Fenchel's hypothesis and the existence of recession directions in convex programming is established and then expressed within each of these three duality formulations Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • Elmor Peterson, 2001. "The Fundamental Relations between Geometric Programming Duality, Parametric Programming Duality, and Ordinary Lagrangian Duality," Annals of Operations Research, Springer, vol. 105(1), pages 109-153, July.
    • Handle: RePEc:spr:annopr:v:105:y:2001:i:1:p:109-153:10.1023/a:1013353515966
    DOI: 10.1023/A:1013353515966
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/A:1013353515966
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/A:1013353515966?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Liu, Shiang-Tai, 2006. "Posynomial geometric programming with parametric uncertainty," European Journal of Operational Research, Elsevier, vol. 168(2), pages 345-353, January.
    2. G. S. Mahapatra & T. K. Mandal, 2012. "Posynomial Parametric Geometric Programming with Interval Valued Coefficient," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 120-132, July.
    3. Frenk, J.B.G. & Kassay, G., 2004. "Introduction to Convex and Quasiconvex Analysis," ERIM Report Series Research in Management ERS-2004-075-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    4. Rashed Khanjani Shiraz & Hirofumi Fukuyama, 2018. "Integrating geometric programming with rough set theory," Operational Research, Springer, vol. 18(1), pages 1-32, April.
    5. S. K. Mishra & Vinay Singh & Vivek Laha, 2016. "On duality for mathematical programs with vanishing constraints," Annals of Operations Research, Springer, vol. 243(1), pages 249-272, August.
    6. R. R. Ota & J. C. Pati & A. K. Ojha, 2019. "Geometric programming technique to optimize power distribution system," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 282-299, March.
    7. Wasim Akram Mandal, 2021. "Weighted Tchebycheff Optimization Technique Under Uncertainty," Annals of Data Science, Springer, vol. 8(4), pages 709-731, December.
    8. Qingjie Hu & Jiguang Wang & Yu Chen, 2020. "New dualities for mathematical programs with vanishing constraints," Annals of Operations Research, Springer, vol. 287(1), pages 233-255, April.
    9. Rashed Khanjani Shiraz & Madjid Tavana & Debora Di Caprio & Hirofumi Fukuyama, 2016. "Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 243-265, July.
    10. Liu, Shiang-Tai, 2008. "Posynomial geometric programming with interval exponents and coefficients," European Journal of Operational Research, Elsevier, vol. 186(1), pages 17-27, April.

    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:annopr:v:105:y:2001:i:1:p:109-153:10.1023/a:1013353515966. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.