IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v99y1998i3d10.1023_a1021763419562.html
   My bibliography  Save this article

Relaxed Cutting Plane Method for Solving Linear Semi-Infinite Programming Problems

Author

Listed:
  • S. Y. Wu

    (National Cheng Kung University)

  • S. C. Fang

    (North Carolina State University)

  • C. J. Lin

    (University of Michigan)

Abstract

One of the major computational tasks of using the traditional cutting plane approach to solve linear semi-infinite programming problems lies in finding a global optimizer of a nonlinear and nonconvex program. This paper generalizes the Gustafson and Kortanek scheme to relax this requirement. In each iteration, the proposed method chooses a point at which the infinite constraints are violated to a degree, rather than a point at which the violations are maximized. A convergence proof of the proposed scheme is provided. Some computational results are included. An explicit algorithm which allows the unnecessary constraints to be dropped in each iteration is also introduced to reduce the size of computed programs.

Suggested Citation

  • S. Y. Wu & S. C. Fang & C. J. Lin, 1998. "Relaxed Cutting Plane Method for Solving Linear Semi-Infinite Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 99(3), pages 759-779, December.
    • Handle: RePEc:spr:joptap:v:99:y:1998:i:3:d:10.1023_a:1021763419562
    DOI: 10.1023/A:1021763419562
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1021763419562
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1021763419562?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. Mohammad R. Oskoorouchi & Hamid R. Ghaffari & Tamás Terlaky & Dionne M. Aleman, 2011. "An Interior Point Constraint Generation Algorithm for Semi-Infinite Optimization with Health-Care Application," Operations Research, INFORMS, vol. 59(5), pages 1184-1197, October.
    2. Li-Ping Pang & Jian Lv & Jin-He Wang, 2016. "Constrained incremental bundle method with partial inexact oracle for nonsmooth convex semi-infinite programming problems," Computational Optimization and Applications, Springer, vol. 64(2), pages 433-465, June.
    3. Mengwei Xu & Soon-Yi Wu & Jane Ye, 2014. "Solving semi-infinite programs by smoothing projected gradient method," Computational Optimization and Applications, Springer, vol. 59(3), pages 591-616, December.
    4. C.F. Wen & S.Y. Wu, 2004. "Duality theorems and algorithms for linear programming in measure spaces," Journal of Global Optimization, Springer, vol. 30(2), pages 207-233, November.
    5. Ralf Werner, 2008. "Cascading: an adjusted exchange method for robust conic programming," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 179-189, June.
    6. Fang, S-C. & Wu, S. & Birbil, S.I., 2002. "Solving variational inequalities defined on a domain with infinitely many linear constraints," Econometric Institute Research Papers EI 2002-51, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Fang, S-C. & Wu, S. & Birbil, S.I., 2002. "Solving Variational Inequalities Defined on A Domain with Infinitely Many Linear Constraints," ERIM Report Series Research in Management ERS-2002-70-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.
    8. Soren Christensen, 2011. "A method for pricing American options using semi-infinite linear programming," Papers 1103.4483, arXiv.org, revised Jun 2011.

    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:99:y:1998:i:3:d:10.1023_a:1021763419562. 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.