关键词: 多阶段随机规划, 二次目标函数, 定量稳定性, Lipschitz连续性

Abstract: Multistage stochastic programs can properly describe complex long-term decision-making problems under uncertainty. We study the quantitative stability of multistage stochastic programs with quadratic objective functions under perturbations of the underlying stochastic processes, which extend the current results for the linear objective functions. We first derive the upper bounds of feasible solutions through parametric programming theories. In order to obtain the Lipschitz continuities of recourse functions, we assume the continuity of the conditional distributions under the Fortet-Mourier metric. With these preparations, we finally establish the Lipschitz continuity of the optimal value function. Our quantitative stability results do not rely on the filtration distance.

Key words: multistage stochastic programming,  , quadratic objective function,  , quantitative stability, Lipschitz continuity