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Stochastic non-linear programming

Published online by Cambridge University Press:  09 April 2009

M. A. Hanson
M. A. Hanson
Affiliation:
Department of Statistics, University of New South Wales
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Although many varied techniques have been proposed for handling deterministic non-linear programming problems there apperars to have been little success in solving the more realistic problem of stochastic non-linear programming, despite the many results that have been obtained for stochastic linear programming. In this paper the stochastic non-linear problem is treated by means of an adaptation of a method used by Berkovitz [1] in obtaining an exiatence theorem for a type of inequality constrained variational problem involving one independent variable. The stochastic programming problem of course involves many independent variables. Necessary conditions are obtained for the existence of a solution of a fairly general type of non-linear problem, and these conditions are shown to be also sufficient for the convex problem. A duality theorem is given for the latter problem.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 3 , August 1964 , pp. 347 - 353
Copyright
Copyright © Australian Mathematical Society 1964

References

[1]Berkovitz, L. D., Variational Methods in Problems of Control and Programming, J. Math. Anal. App. 3 (1961) 145–169.CrossRefGoogle Scholar
[2]Kuhn, H.W., and Tucker, A. W., Non-Linear Programming, Proc. Second Berkeley Symp. on Math. Stats. and Prob., Univ. Calif. Press 1951.Google Scholar
[3]Bliss, G. A., Lectures on the Calculus of Variations, University of Chicago Press, Phoenix Edition 1961.Google Scholar