This paper studies a class of two-stage distributionally robust optimization (TDRO) problems which comes from many practical application fields. In order to set up some implementable solution method, we first transfer the TDRO problem to its equivalent robust counterpart (RC) by the duality theorem of optimization. The RC reformulation of TDRO is a semi-infinite stochastic programming. Then we construct a conditional value-at-risk-based sample average approximation model for the RC problem. Furthermore, we analyse the error bound of the approximation model and obtain the convergent results with respect to optimal value and optimal solution set. Finally, a so-called stochastic dual dynamic programming approach is proposed to solve the approximate model. Numerical results validate the solution approach of this paper.

本文研究了来自许多实际应用领域的一类两阶段分布鲁棒优化（TDRO）问题。为了建立一些可行的解决方法，我们首先通过优化对偶定理将TDRO问题转移到其等效的鲁棒对应项（RC）。TDRO的RC重新编制是一种半无限随机编程。然后，我们为RC问题构建了基于条件风险值的样本平均逼近模型。此外，我们分析了近似模型的误差范围，并获得了关于最优值和最优解集的收敛结果。最后，提出了一种所谓的随机双重动态规划方法来求解近似模型。数值结果验证了本文的求解方法。