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Solving Nonlinear Programming Problems with Stochastic Objective Functions

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  • Ziemba, William T.

Abstract

In many nonlinear programming applications the objective function has an inherent uncertainty that depends upon a set of random variables that have a known distribution. If one wishes to optimize the expectation of the objective, as suggested by the expected utility theorem, then as is shown here one can often solve such problems by modifying standard nonlinear programming algorithms. To illustrate what is involved, the details and justification for the application of the interior parametric sequential unconstrained maximization technique and the generalized programming method for the solution of such problems are given. Some related problems with stochastic constraints for which the solution method applies are mentioned and an example of a portfolio selection problem is given.

Suggested Citation

  • Ziemba, William T., 1972. "Solving Nonlinear Programming Problems with Stochastic Objective Functions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(3), pages 1809-1827, June.
    • Handle: RePEc:cup:jfinqa:v:7:y:1972:i:03:p:1809-1827_01
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    Cited by:

    1. Darlington, J. & Pantelides, C. C. & Rustem, B. & Tanyi, B. A., 2000. "Decreasing the sensitivity of open-loop optimal solutions in decision making under uncertainty," European Journal of Operational Research, Elsevier, vol. 121(2), pages 343-362, March.

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