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Nonlinear Programming Problems with Stochastic Objective Functions

Author

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  • 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
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    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.

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