SOLVING NONLINEAR PROGRAMMING PROBLEMS WITH STOCHASTIC OBJECTIVE FUNCTIONS

William T. Ziemba

Chapter 2 in Selected Works of William T Ziemba:A Memorial Volume, 2024, pp 25-43 from World Scientific Publishing Co. Pte. Ltd.

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.

Keywords: William Ziemba; Financial Planning Models; Racetrack Betting; Sports Analytics; Market Anomalies; Risk Factors (search for similar items in EconPapers)
JEL-codes: C44 C6 G11 G12 (search for similar items in EconPapers)
Date: 2024
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