Abstract
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.
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