决策依赖模糊集下的分布鲁棒优化的重构
Reconstruction of Distributed Robust Optimization under Decision-Dependent Ambiguity Set

本文考虑一类分布鲁棒优化问题，其中随机变量的概率分布依赖于决策变量。模糊集由带有参数均值和协方差矩阵的集合定义，且不确定参数的均值与决策相关。当支撑集为全空间时，本文利用Lagrange对偶理论证明了原问题等价于半定规划问题，且可以转化成形式更简单的非光滑凸问题，进而可得到为更易处理的二阶锥优化问题。
In this paper we consider a class of Distributionally Robust Optimization (DRO) Problems where the probability distribution of random variables depends on decision variables and the ambiguity set is defined through a set with parameter mean and covariance matrix, and the mean of uncertain pa-rameters is dependent on decision. Under the condition of the support set is the whole space, We demonstrate the original problem is equivalent to the semidefinite programming problem by using Lagrange duality theory. Moreover, it can be transformed into a simpler form of non-smooth convex problem, and we further obtain a more tractable second-order cone optimization.