We study the distributionally robust stochastic optimization problem within a general framework of risk measures, in which the ambiguity set is described by a spectrum of practically used probability distribution constraints such as bounds on mean-deviation and entropic value-at-risk. We show that a subgradient of the objective function can be obtained by solving a finite-dimensional optimization problem, which facilitates subgradient-type algorithms for solving the robust stochastic optimization problem. We develop an algorithm for two-stage robust stochastic programming with conditional value at risk measure. A numerical example is presented to show the effectiveness of the proposed method.

中文翻译：

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具有凸风险测度的鲁棒随机优化：离散次梯度方案

我们在风险度量的一般框架内研究了分布鲁棒的随机优化问题，其中歧义集由一系列实际使用的概率分布约束（例如均值偏差边界和熵风险值）来描述。我们表明，可以通过解决有限维优化问题来获得目标函数的次梯度，这有利于次梯度型算法用于解决鲁棒随机优化问题。我们开发了一种具有条件价值风险度量的两阶段鲁棒随机规划算法。数值例子表明了该方法的有效性。