IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v10y1964i2p353-359.html
   My bibliography  Save this article

Nonlinear Programming Problems with Stochastic Objective Functions

Author

Listed:
  • O. L. Mangasarian

    (Shell Development Company, Emeryville, California)

Abstract

In many optimization problems the objective function may depend on a random set of coefficients that have some known distribution. For example, a profit function may depend on certain market conditions which can at best be estimated by a set of random variables with some given distribution. An important question to be answered in such problems is: What is the expected value of the maximum profit? On the answer to this question may hinge certain very important decisions that an organization may have to make. It may also provide good estimates of future profits. While the problem of determining the expected value of the maximum may be very difficult at times, a number of related problems, some quite important in their own right, may be considerably easier to solve and also may provide bounds for the expected value of the maximum. In this work, one upper and three lower bounds are given in terms of the solutions of related problems. In addition a convexity property for a class of parametric nonlinear programming problems is obtained. This property is also used in deriving some of the bounds.

Suggested Citation

  • O. L. Mangasarian, 1964. "Nonlinear Programming Problems with Stochastic Objective Functions," Management Science, INFORMS, vol. 10(2), pages 353-359, January.
    • Handle: RePEc:inm:ormnsc:v:10:y:1964:i:2:p:353-359
    DOI: 10.1287/mnsc.10.2.353
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.10.2.353
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.10.2.353?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
    ---><---

    Citations

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


    Cited by:

    1. Akif Bakir, M. & Byrne, Mike D., 1998. "Stochastic linear optimisation of an MPMP production planning model," International Journal of Production Economics, Elsevier, vol. 55(1), pages 87-96, June.
    2. Benjamin F. Hobbs & Yuandong Ji, 1999. "Stochastic Programming-Based Bounding of Expected Production Costs for Multiarea Electric Power System," Operations Research, INFORMS, vol. 47(6), pages 836-848, December.
    3. Robert Inman, 1981. "On setting the agenda for Pennsylvania school finance reform: An exercise in giving policy advice," Public Choice, Springer, vol. 36(3), pages 449-474, January.

    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:inm:ormnsc:v:10:y:1964:i:2:p:353-359. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.