Abstract We considers a distributionally robust optimization problem when the ambiguity set specifies the support as well as the mean and the covariance matrix of the uncertain parameters. After deriving a general deterministic reformulation for the distributionally robust optimization problem, we obtain tractable optimization reformulations when the support set is the whole space and when it is a convex polyhedral set. A hybrid method of Gurobi and a smoothing Newton conjugate gradient method is suggested to solve the tractable optimization problems and numerical results of the hybrid method for solving an illustrative example are reported.

中文翻译：

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关于矩不确定下分布鲁棒优化的说明

摘要 当模糊集指定支持以及不确定参数的均值和协方差矩阵时，我们考虑分布鲁棒优化问题。在推导出分布鲁棒优化问题的一般确定性重构之后，当支持集是整个空间并且它是凸多面体集时，我们获得了易于处理的优化重构。提出了 Gurobi 的混合方法和平滑牛顿共轭梯度方法来解决易处理的优化问题，并报告了解决说明性示例的混合方法的数值结果。