Probability approximation schemes for stochastic programs with distributionally robust second-order dominance constraints
Probability approximation schemes for stochastic programs with distributionally robust second-order dominance constraints
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DOI：
10.1080/10556788.2016.1175003
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发表时间：
2017-07
影响因子：
2.2
通讯作者：
Shaoyan Guo;Huifu Xu;Liwei Zhang
中科院分区：
文献类型：
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作者：
Shaoyan Guo;Huifu Xu;Liwei Zhang
由于Dentcheva和Ruszczyovski的开创性工作[具有随机优势约束的优化，SIAM J. Optim. 14（2003），pp. 548-566]，二阶优势约束随机规划（SPSODC）在过去的十年中得到了广泛的讨论，从最优性理论到数值格式和实际应用。在本文中，我们研究离散逼近SPSODC时（a）的真实概率是已知的，但连续分布和（B）的真实概率分布是未知的，但它位于一个模糊的分布集。不同于众所周知的蒙特卡洛离散化方法，我们提出了一种确定性离散近似方案，这是由于Pflug和Pichler [Approximations for Probability Distributions and Stochastic Optimization Problems，International Series in Operations Research & Management Science，Vol.163，Springer，纽约，2011，pp. 343-387]，并证明了离散概率测度和离散概率测度的模糊集在Kantorovich度量下近似于它们的连续对应物。稳定性分析的最优值和最优解所产生的离散优化问题和一些比较数值试验结果的报告。
Since the pioneering work by Dentcheva and Ruszczyński [Optimization with stochastic dominance constraints, SIAM J. Optim. 14 (2003), pp. 548–566], stochastic programs with second-order dominance constraints (SPSODC) have received extensive discussions over the past decade from theory of optimality to numerical schemes and practical applications. In this paper, we investigate discrete approximation of SPSODC when (a) the true probability is known but continuously distributed and (b) the true probability distribution is unknown but it lies within an ambiguity set of distributions. Differing from the well-known Monte Carlo discretization method, we propose a deterministic discrete approximation scheme due to Pflug and Pichler [Approximations for Probability Distributions and Stochastic Optimization Problems, International Series in Operations Research & Management Science, Vol. 163, Springer, New York, 2011, pp. 343–387] and demonstrate that the discrete probability measure and the ambiguity set of discrete probability measures approximate their continuous counterparts under the Kantorovich metric. Stability analysis of the optimal value and optimal solutions of the resulting discrete optimization problems is presented and some comparative numerical test results are reported.