一类分布鲁棒线性决策随机优化研究

随机优化广泛应用于经济、管理、工程和国防等领域,分布鲁棒优化作为解决分布信息模糊下的随机优化问题近年来成为学术界的研究热点.本文基于φ-散度不确定集和线性决策方式研究一类分布鲁棒随机优化的建模与计算,构建了易于计算实现的分布鲁棒随机优化的上界和下界问题.数值算例验证了模型分析的有效性.

The Study of Stochastic Optimization for Linear Decision Rule in a Class Distributionally Robustness

Stochastic optimization has wide applications in a lot of areas,such as economic,management,engineering,and national defense.As a kind of stochastic optimization problem to solve the distributed information fuzzy,distributionally robust optimization has become a research hotspot in academics in recent years,but it can be computationally complex when the recourse decisions are modeled as decision rules,i.e.,functions of the random variable.It had been argued that stochastic programs can quite generally be made tractable by restricting the space of decision rules to those that exhibit a linear data dependence.In this paper,it is based on the φ-divergence uncertain set and linear decision method to research the modeling and calculation of distributionally robust stochastic optimization problem.We apply the linear decision rules to both original and dual versions of the distributionally robust optimization,which is developed the main idea to distributionally robust optimization in Kuhn D,Wiesemann W,Georghiou A.Primal and dual linear decision rules in stochastic and robust optimization.Mathematical Programming,2011,130(1):177-209.By employing the optimal theorems and methods,we construct the upper and lower bounds problem which make the distributionally robust stochastic optimization be easily calculated.The experiments of the numerical value demonstrate the validity of the model analysis.