We consider a two-stage stochastic variational inequality arising from a general convex two-stage stochastic programming problem, where the random variables have continuous distributions. The equivalence between the two problems is shown under some moderate conditions, and the monotonicity of the two-stage stochastic variational inequality is discussed under additional conditions. We provide a discretization scheme with convergence results and employ the progressive hedging method with double parameterization to solve the discretized stochastic variational inequality. As an application, we show how the water resources management problem under uncertainty can be transformed from a two-stage stochastic programming problem to a two-stage stochastic variational inequality, and how to solve it, using the discretization scheme and the progressive hedging method with double parameterization.

中文翻译：

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由随机规划引起的两阶段随机变分不等式

我们考虑由一般凸两阶段随机规划问题引起的两阶段随机变分不等式，其中随机变量具有连续分布。两个问题之间的等价性在一些温和的条件下显示，并在附加条件下讨论了两阶段随机变分不等式的单调性。我们提供了一个具有收敛结果的离散化方案，并采用具有双参数化的渐进对冲方法来解决离散化的随机变分不等式。作为一个应用，我们展示了不确定性下的水资源管理问题如何从两阶段随机规划问题转化为两阶段随机变分不等式，以及如何解决它，