Abstract In this paper, we consider the optimization problems with k-th order stochastic dominance constraint on the objective function of the two-stage stochastic programs with full random quadratic recourse. By establishing the Lipschitz continuity of the feasible set mapping under some pseudo-metric, we show the Lipschitz continuity of the optimal value function and the upper semicontinuity of the optimal solution mapping of the problem. Furthermore, by the Holder continuity of parameterized ambiguity set under the pseudo-metric, we demonstrate the quantitative stability results of the feasible set mapping, the optimal value function and the optimal solution mapping of the corresponding distributionally robust problem.

中文翻译：

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关于由完全随机二次资源引起的具有k阶随机优势约束的分布鲁棒优化问题

摘要 在本文中，我们考虑了具有完全随机二次资源的两阶段随机程序的目标函数上具有k阶随机优势约束的优化问题。通过建立一些伪度量下可行集映射的Lipschitz连续性，我们证明了最优值函数的Lipschitz连续性和问题最优解映射的上半连续性。此外，通过伪度量下参数化模糊集的Holder连续性，我们证明了对应分布鲁棒问题的可行集映射、最优值函数和最优解映射的定量稳定性结果。