求解含非离散分布的分布鲁棒多阶段线性随机规划的Benders分解-动态逼近方法

本文对包含非离散分布的一类分布鲁棒多阶段随机线性规划问题提出了一种基于Benders分解的动态逼近方法. 在随机因素按阶段独立、分布模糊集由矩约束给出等条件下, 利用Benders分解构建了各阶段决策函数的近似函数, 从而将多阶段决策问题近似分解为一系列具有锥约束形式的凸优化子问题. 为分析算法的收敛性, 本文构建了一个新的基于变分分析的收敛性分析框架, 并证明了算法构建的近似问题对原问题具有上图收敛性. 最后通过数值试验展示了算法的有效性.

An approximate dynamic Benders decomposition method is proposed for solving the distributionally robust multistage stochastic linear optimization problem, in which the random parameters are allowed to be nondiscrete. The random parameters are assumed to be stage-wise independent and the ambiguity set of the probability distribution is described by moment constraints. Under these assumptions, the Benders decomposition is used to construct the approximations of the cost-to-go functions of each stage so that the multistage problem can be approximately decomposed to a series of convex subproblems with conic constraints. To establish the convergence of the algorithm, a new analysis framework based on variational analysis is established, and the approximated problems are shown to have epi-convergence towards their original counterparts. Finally, the effectiveness of the algorithm is demonstrated via numerical experiments.